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Full text of "Isokinetic sampling of aerosols from tangential flow streams"

ISOKINETIC SAMPLING OF AEROSOLS FROM 
TANGENTIAL FLOW STREAMS 



By 



Michael Dean Durham 



A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF 

THE UNIVERSITY OF FLORIDA 
IN PARTIAL FULFILLMENT OF THE 'REQUIRE^ENTS FOR THE 
DEGREE OF DOCTOR OF PHILOSOPHY 



UNIVERSITY OF FLORIDA 
1978 



ACKNOWLEDGEMENTS 

This research was partially supported by a grant (Grant Number 
R802692-01) from the Environmental Protection Agency (EPA)-, and was 
monitored by EPA's Project Officer Kenneth T. Knapp. I thank them 
both for their financial support during my graduate work. 

I wish to thank Dr. Dale Lundgren and Dr. Paul Urone for the 
important part that they played in my education. I am especially 
appreciative of Dr. Lundgren for his guidance, encouragement and 
confidence. He has provided me witli opportunities for classroom, 
laboratory and field experience that were far beyond what is expected 
of a committee chairman. 

1 would like to thank Mrs. Kathy Sheridan for her assistance in 
preparing this manuscript. 

Finally, I wish to thank my parents for their advice and encourage- 
ment, and my wife Ellie for helping me through the difficult times. 



11 



TABLE OF CONTENTS 



Page 



ACKNOWLEDGEMENTS ii 

LIST OF TABLES v 

LIST OF FIGURES viii 

LIST OF SYMBOLS xi 

ABSTRACT xiii 

CHAPTER 

I INTRODUCTION AND ISOKINETIC SAMPLING THEORY 1 

A. Introduction 1 

B. Isokinetic Sampling Theory 2 

II REVIEW OF THE PERTINENT LITERATURE 10 

A. Summary of the Literature on Anisokinetic Sampling. . . 10 

1. Sampling Bias Due to Unmatched Velocities 10 

2. Sampling Bias Due to Nozzle Misalignment 17 

B. Summary of the Literature on Tangential Flow 23 

1. Causes and Characteristics of Tangential Flow 23 

2 . Errors Induced by Tangential Flow 31 

3. Errors Due to the S-Type Pitot Tube 35 

4. Methods Available for Measuring Velocity 

Components in a Tangential Flow Field 41 

5. EPA Criteria for Sampling Cyclonic Flow 43 

in EXPERIMENTAL APPARATUS AND METHODS 48 

A. Experimental Design 48 

B. Aerosol Generation 51 

1 . Spinning Disc Generator 51 

2. Ragweed Pollen 53 

C. Velocity Determination 53 

D. Selection of Sampling Locations 57 

E. Sampling Nozzles 57 



111 



TABLE OF CONTENTS --continued 



CHAPTER Page 



F. Analysis Procedure 58 

1 . For Uranine Particles 58 

2. For Ragweed Pollen 58 

G. Sampling Procedure 59 

H. Tangential Flow Mapping 60 

IV RESULTS AND ANALYSIS 65 

A. Aerosol Sampling Experiments 65 

1 . Stokes Number 65 

2. Sampling with Parallel Nozzles 66 

3. Analysis of Probe Wash 66 

4. The Effect of Angle Misalignment on Sampling 
Efficiencies 69 

5. The Effect of Nozzle Misalignment and Anisokinetic 
Sampling Velocity 89 

B. Tangential Flow Mapping 102 

V SIMULATION OF AN EPA METHOD 5 EMISSION TEST IN A TANGENTIAL 
FLOW STREAjM 117 

VI SUMMARY AND RECOMMENDATIONS 129 

A. Summary 129 

B. Recommendations 134 

REFERENCES 135 

BIOGRAPHICAL SKETCH 139 



IV 



LIST OF Ty\BLES 
Table Page 

I FLOW RATE DETERMINED AT VARIOUS MEASUREMENT LOCATIONS 33 

II CONCENTRATION AT A POINT FOR DIFFERENT SAMPLING ANGLES 34 

III EMISSION TEST RESULTS 36 

IV SIZES AND DESCRIPTIONS OF EXPERIMENTAL AEROSOLS 52 

V TABLE OF OBTAINABLE VELOCITIES IN 10 cm DUCT. 54 

VI TYPICAL VELOCITY TRAVERSE IN THE EXPERIMENTAL SAJ-IPLING 
SYSTEM 55 

VII RESULTS OF SAMPLING WITH TWO PARALLEL NOZZLES 67 

VIII PERCENT OF PARTICULATE MATTER COLLECTED IN THE PROBE WASH 

FOR NOZZLES PARALLEL WITH THE FLOW STREAM 68 

IX PERCENT OF PARTICULATE MATTER COLLECTED IN THE PROBE WASH 

FOR NOZZLES AT AN ANGLE OF 60 DEGREES WITH THE FLOW STREAiM. 70 

X ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER FOR 

30 DEGREE MISALIGNMENT 75 

XI ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER FOR 

60 DEGREE MISALIGNMENT 77 

XII ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER FOR 

90 DEGREE MISALIGNMENT 80 

XIII COMPARISON OF SAMPLING EFFICIENCY RESULTS WITH THOSE OF 
BELYAEV AND LEVIN FOR 6 = , R = 2 . 3 AND R = 0.5 92 

XIV ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER FOR 

R = 2, = 60 94 



LIST OF TABLES- -continued 



Table Pape 



XV ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER 

FOR R = 0.5, 6 = 60° 95 

XVI ASPIR./\TION COEFFICIENT AS A FUNCTION OF STOKES NUMBER 

FOR e = 45°, R = 2.0 AND 0.5 97 

XVII ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER 

FOR R = 2, 6 = 30° 98 

XVIII ASPIRATION COEFFICIENT AS A FUNCTION OF STOKES NUMBER 

FOR R = 2.1, e = 90° 101 

XIX LOCATION OF SAMPLING POINTS 105 

XX FIVE-HOLE PITOT TUBE MEASUREMENTS MADE AT 1 DIAMETER 
DOWNSTREAM OF THE CYCLONE 106 

XXI FIVE-HOLE PITOT TUBE MEASUREMENTS MADE AT 2 DIAMETERS 
DOWNSTREAM OF THE CYCLONE 107 

XXII FIVE-HOLE PITOT TUBE MEASURENffiNTS MADE AT 4 DIAMETERS 
DOWNSTREAM OF THE CYCLONE 108 

XXIII FIVE-HOLE PITOT TUBE MEASUREMENTS MADE AT 8 DIAMETERS 
DOWNSTREAI'l OF THE CYCLONE 109 

XXIV FIVE -HOLE PITOT TUBE MEASUREMENTS MADE AT 16 DIAMETERS 
DOIVNSTREAM OF THE CYCLONE 110 

XXV AVERAGE CROSS SECTIONAL VALUES AS A FUNCTION OF DISTANCE 
DOWNSTREAM AND FLOW RATE 112 

XXVI S-TYPE PITOT TUBE MEASUREMENTS MADE AT THE 8-D SAiMPLING 

PORT FOR THE LOW FLOW CONDITION 118 

XXVII S-TYPE PITOT TUBE MEASUREMENTS MADE AT THE 8-D S.-UIPLING PORT 

FOR THE HIGH FLOW CONDITION 119 

XXVIII MIDPOINT PARTICLE DIAMETERS FOR THE 10 PERCENT INTERVALS 

OF THE MASS DISTRIBUTION MMD = 3ym a = 2.13 121 



VI 



.-S'^l- •^=^^S^ ...MS^L ^ 



LIST OF TABLES--continued 



Table 



Page 



XXIX ASPIRATION COEFFICIENTS CALCULATED IN THE SIMULATION 

MODEL FOR THE LOW FLOW CONDITION 124 

XXX ASPIRATION COEFFICIENTS CALCULATED IN THE SIMULATION 

MODEL FOR THE HIGH FLOW CONDITION 125 

XXXI RESULTS OF THE CYCLONE OUTLET SIMULATION MODEL FOR THREE 
CONDITIONS 127 

XXXII SUMMARY OF EQUATIONS PREDICTING PARTICLE SA^1PLING BIAS 128 



VI 1 



LIST OF FIGURES 

Figure Page 

1 Isokinetic sampling 3 

2 Superisokinetic sampling 4 

3 Subisokinetic sampling 6 

4 The effect of nozzle misalignment with flow stream 7 

5 Relationship between the concentration ratio and the 
velocity ratio for several size particles 11 

6 Sampling efficiency as a function of Stokes number and 
velocity ratio 16 

7 Error due to misalignment of probe to flow stream IS 

8 Sampling bias due to nozzle misalignment and anisokinetic 
sampling velocity 21 

9 Tangential flow induced by ducting 25 

10 Double vortex flow induced by ducting 26 

11 Velocity components in a swirling flow field 27 

12 Cross sectional distribution of tangential velocity in a 
swirling flow field 29 

13 Cross sectional distribution of angular momentum in a 
swirling flow field 30 

14 S-type pitot tube with pitch and yaw angles defined 38 

15 Velocity error vs. yaw angle for an S-type pitot tube.... 39 

16 Velocity error vs. pitch angle for an S-type pitot tube.. 40 



Vlll 



LIST OF FIGURES--continued 

Figure Page 

17a Conical version of a five-hole pitot tube 42 

17b Fecheimer type three-hole pitot tube 42 

18 Five-hole pitot tube sensitivity to yaw angle 44 

19 Fecheimer pitot tube sensitivity to yaw angle 45 

20 Experimental set up 49 

21 Sampling system 50 

22 Typical velocity profile in experimental test section.... 56 

23 Experimental system for measuring cross sectional flow 
patterns in a swirling flow stream 61 

24 Cyclone used in the study to generate swirling flow 62 

25 Photograph of the 3-dimensional pitot with its traversing 
unit. Insert shows the location of the pressure taps.... 63 

26 Sampling efficiency vs. Stokes number at 30° misalignment 

for R = 1 72 

27 Sampling efficiency vs. Stokes number at 60° misalignment 

for R = 1 73 

28 Sampling efficiency vs. Stokes number at 90° misalignment 

for R = 1 74 

29 Stokes number at which 95% maximum error occurs vs. 
misalignment angle 83 

30 6' vs. adjusted Stokes number for 30, 60 and 90 degrees.. 85 

31 Aspiration coefficient vs. Stokes number - model predic- 
tion and experimental data for 30, 60 and 90 degrees 87 

32 Predicted aspiration coefficient vs. Stokes number for 

15, 30, 45, 60, 75 and 90 degrees 88 



IX 



LIST OF FIGURES--continued 



Figure Page 



33 Comparison of experimental data with results from Belyaev 

and Levin 91 

34 Sampling efficiency vs. Stokes number at 60° misalignment 

for R = 2.0 and 0.5 96 

35 Sampling efficiency vs, Stokes number at 45° misalignment 

for I^ = 2.0 and R = 0.5 99 

36 Sampling efficiency vs. Stokes number at 30° misalignment 

for U = 2.0 100 

37 Cross sectional view of a tangential flow stream locating 
pitch and yaw directions, sampling points, and the nega- 
tive pressure region 105 

38 Decay of the average angle 9 and the core area along the 

axis of the duct 113 

39 Decay of the tangential velocity component along the axis 

of the duct 114 

40 Location of the negative pressure region as a function of 
distance downstream from the cyclone 116 

41 Particle size distributions used in the simulation model... 120 



■^! W^ ^t^rTJ^U^^*"*— T'^-t-*.'** i."* ' '^ i» *- '«"'*-i**I-V»t'*'* 



SYMBOLS 

A. - area of sampler inlet 

A '- projected area of sampler inlet 

A^ - area of stream tube approaching nozzle 

A - ratio of measured concentration to true concentration 

C - Cunningham correction factor 

C. - dust concentration in inlet 

Cq - dust concentration in flow stream 

C 
r - concentration ratio of aerosol generating solution 

D, - droplet diameter 
D. - inlet diameter 



'S 



1 



D - particle diameter 

K - inertial impaction parameter 

K' - adjusted Stokes number 

i - stopping distance 

L - undisturbed distance upstream from nozzle 

n - constant 

R - ratio of free stream velocity to inlet velocity 

s - constant 

V - axial component of stack velocity 

V - velocity in inlet 

^r ~ radial component of stack velocity 
V^ - free stream velocity 



XI 



V^ - tangential component of stack velocity 

&, 3', 6" - functions determining whether particles will deviate from 
streamlines 

P - particle density 

n - viscosity 

^ - angle of the flow stream with respect to the stack axis 

e - angle of misalignment of nozzle with respect to the flow stream 

T - particle relaxation time 

Ap - pressure difference 



Xll 



Abstract of Dissertation Presented to the Graduate Council 
of the University of Florida in Partial Fulfillment of the 
Requirements for the Degree of Doctor of Philosophy 

ISOKINETIC SAMPLING OF AEROSOLS FROM TANGENTIAL FLOW STREAMS 

By 
Michael D. Durham 
August, 1978 

Chairman: Dale A. Lundgren 

Major Department: Environmental Engineering Sciences 

A comprehensive analysis of inertial effects in aerosol sampling was 
combined with a thorough study of swirling flow patterns in a stack fol- 
lowing the exit of a cyclone in order to determine the errors involved in 
sampling particulate matter from a tangential flow stream. Two simultaneous 
samples, one isokinetic and the other anisokinetic , were taken from a 10 cm 
wind tunnel and compared to determine sam.pl ing bias as a function of Stokes 
number. Monodispersed uranine particles, 1 to 11 pm in diameter, generated 
with a spinning disc aerosol generator, and mechanically dispersed 19.9 pm 
ragween pollen were used as experimental aerosols. The duct velocity was 
varied from 550 to 3600 cm/sec and two nozzle diameters of 0.465 and 0.6S3 
cm were used to obtain values of Stokes numbers from 0.007 to 2.97. Experi- 
ments were performed at four angles, 0, 30, 60 and 90 degrees, to determine 
the errors encountered when sampling with an isokinetic sampling velocity 
but with the nozzle misaligned with the flow stream. The sampling bias ap- 
proached a theoretical limit of (l-cosG) at a value of Stokes number between 



Xlll 



•(4=*— M *=-<^»ti-:- -a Wi 



1 and 6 depending on the angle of misalignment. It was discovered that the 
misalignment angle reduces the projected nozzle diameter and therefore ef- 
fects the Stokes number; a correction factor as a function of angle was 
developed to adjust the Stokes number to account for this. 

Using an equation empirically developed from these test results and 
using the equations of Belyaev and Levin describing anisokinetic sampling 
bias with zero misalignment, a mathematical model was developed and tested 
which predicts the sampling error when both nozzle misalignment and aniso- 
kinetic sampling velocities occur simultaneously. It was found that the 
sampling bias approached a maximum error |l-Rcos0| where R is the ratio of 
the free stream velocity to the sampling velocity. During the testing, it 
was discovered that as much as 60% of the particulate matter entering the 
nozzle remained in the nozzle and front half of the filter holder. Implica- 
tions of this phenomenon with regard to particle sampling and analysis are 
discussed . 

The causes and characteristics of tangential flow streams are described 
as they relate to problems in aerosol sampling. The limitations of the S-type 
pitot tube when used in a swirling flow are discussed. A three dimensional or 
five-hole pitot tube was used to map cross sectional and axial flow patterns 
in a stack following the outlet of a cyclone. Angles as great as 70 degrees 
relative to the axis of the stack and a reverse flow core area were found in 
the stack. 

Using information found in this study, a simulation model was developed 
to determine the errors involved when making a Method 5 analysis in a tan- 
gential flow stream. For an aerosol with a 3.0 ym MMD (mass mean diameter) 



XIV 



and geometric standard deviation (o ) of 2.13, the predicted concentration 
was 10-5 less than the true concentration. For an aerosol with a 10.0 ym ^C^1D 
and a a of 2.3, a 20% error was predicted. Flow rates determined by the 
S-type pitot tube were from 20 to 30-5 greater than the actual flow rate. 
Implications of these results are described and recommendations for modifica- 
tion of the Method 5 sampling train for use in a tangential flow stream are 
described. 



XV 



• •is^m^'-'itix^i^ 



CHAPTER I 
INTRODUCTION AND ISOKINETIC SAMPLING THEORY 



A. Introduction 



This study deals with the problems of obtaining a representative 
sample of particulate matter from a gas stream that does not flow 
parallel to the axis of the stack as in the case of swirling or 
tangential flow. This type of flow is commonly found in stacks and 
could be the source of substantial sampling error. The causes and 
characteristics of this particular flow pattern are described and 
the errors encountered in particulate concentration and emission 
rate determinations are thoroughly analyzed and discussed. 

The analysis of sampling errors is approached from two directions 
in this study. One approach involves an investigation of aerosol 
sampling bias due to anisokinetic sampling velocities and misalignment 
of the nozzle with respect to the flow stream as a function of particle 
and flow characteristics. The second part of the study involves an 
accurate mapping of the flow patterns in a tangential flow system. 
The information obtained in the two parts of the study will be combined 
to simulate the errors that would be encountered when making an EPA 
Method 5 (1, 2) analysis in a tangential flow stream. 



, fc-,i^.Mfin»H'jt-^'r 



B. isokinetic S ampling Theory 

To obtain a representative sample of particulate matter from a 

moving fluid, it is necessary to sample isokinetically . Isokinetic 

sampling can be defined by two conditions: [3} 1) The suction or 

nozzle velocity, V., must be equal to the free stream velocity, V ; 

1 ■ o 

and 2) the nozzle must be aligned parallel to the flow direction. 

If these conditions are satisfied the frontal area of the nozzle, A , 

1 

will be equal to the area of the cross section of the flow stream 

entering the nozzle, A^ (see Figure 1). Thus, there will be no 

divergence of streamlines either away from or into the nozzle, and 

the particle concentration in the inlet, C, will be equal to the 

particle concentration in the flow stream, C . 

o 

When divergence of streamlines is produced by superisokinetic 

sampling, subisokinetic sampling or nozzle misalignment, there is a 

possibility of particle size fractionation due to the inertial 

properties of particles. In the case of superisokinetic sampling 

[see Figure 2), the sampling velocity, V., is greater than the free 

stream velocity, V^ . Therefore, the area of the flow stream that is 

sampled, A^ ' , will be greater than the, frontal area of the sampling 

nozzle, A . All of the particles that lie in the projected area A.' 

will enter into the nozzle. Particles outside this area but within A 

o 

will have to turn with the streamlines in order to be collected. Be- 
cause of their inertia, some of the larger particles will be unable to 
make the turn and will not enter the sampling nozzle. Since not all of 
the particles in the sampled area A will be collected, the measured 
concentration will be less than the actual concentration. 




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Subisokinetic sampling defines the condition in which the sampling 
velocity is less than the free stream velocity (see Figure 5) . In this 
situation the frontal area of the nozzle. A.', is greater than the sam- 
pled area of the flow, A^ . The volume of air lying within the projected 
area, A^ ' , but outside A will not be sampled and the streamlines will 
diverge around the nozzle. However, some of the particles in this area, 
because of their inertia, will be unable to negotiate the turn with the 
streamlines and will be collected in the nozzle. Because some of the 

particles outside the sampled area A will be collected along with all 

o '^ 

of the particles within A the measured concentration will be greater 
than the actual particle concentration. 

The bias due to misalignment of the nozzle with the flow stream 
is similar to that caused by superisokinetic sampling. When the nozzle 
is at an angle to the flow stream (Figure 4), the projected area of the 
nozzle is reduced by a factor equal to the cosine of the angle. Even 
if the nozzle velocity is equal to the flow stream velocity, a reduced 
concentration will be obtained because some of the larger particles 
will be unable to make the turn into the nozzle with the streamlines. 
Therefore, whenever the nozzle is misaligned, the concentration col- 
lected will always be less than or equal to the actual concentration. 

For all three conditions of anisokinetic sampling (superisokinetic, 
subisokinetic and nozzle misalignment] , the magnitude of the measured 
concentration error will depend upon the size of the particles. More 
specifically it will depend upon particle inertia, which implies that 
the velocity and density of the particle are also important. Particle 



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inertia affects the ability of the particle to negotiate turns with 
its streamline which determines the amount of error. Therefore, in 
all cases greater sampling errors will occur for larger particles and 
higher velocities. 

Besides determining the direction of the sampling bias, it is 
also possible to predict theoretically the minimum and maximum error 
for a given condition. This can be done by considering what happens 
when the inertia of the particles is very small (i.e., the particles 
can negotiate any turn that the streamlines make] and what happens 
when the inertia of particles is very large (i.e., the particles are 
unable to negotiate any turn with the streamlines) . In the former 
case of very low inertia, it can easily be seen that since the particles 
are very mobile they do not leave their streamlines and therefore there 
will be no sampling bias. In this situation the concentration of 
particulate matter may be accurately obtained regardless of sampling 
velocity or whether the nozzle is aligned with the flow stream. There- 
fore, a minimum error of is obtained for small inertia particles. 
The maximum error that can theoretically occur in anisokinetic 
sampling depends on both the velocity ratio R, where 

f^ = \/\ CD 

and the misalignment angle 9. 

In the case of unequal velocities for very high inertia particles 

which are unable to negotiate any change of direction, only those 

particles directly in front of the projected area of the nozzle, A 

i' 

will enter the nozzle regardless of the sampling velocity. Therefore, 



the concentration collected by the nozzle will be equal to the number 

of particles entering the nozzle, A.V C , divided bv the volume of 

1 o o 

air sampled, A.V. . 
1 1 

A.V C C V 

r- 10 o o 

^i = -icvr = T- (2) 

11 1 
The ratio of the sampled concentration to the true concentration then 
is equal to the inverse of the velocity ratio. Therefore, the maximum 
sampling bias for the condition of unmatched velocities is equal to 
V^/V^ or R. For example, if the sampling velocity is twice the free 
stream velocity, the resulting concentration will be one half the actual 
concentration. 

For the case of a misaligned nozzle, a similar analysis is applied. 
For the particles with very large inertia, only those lying directly in 
line with the projected frontal area of the nozzle will be collected. 
The measured concentration would again be the number of particles col- 
lected in the nozzle, A^cosBC^V^, divided by the volume of air sampled, 
A^V^. Therefore, the ratio of the measured to the true concentration 
would be V^cose/V^ or RcosB. This represents the maximum sampling 
error for anisokinetic sampling. 



CHAPTER II 
REVIEW OF THE PERTINENT LITERATURE 



A^__Summa£)^^f^^ on Anisokinet ic Sampling 

j^. Sampling Bia s Due to Unmatched Velocities 

Numerous articles have been written describing the sources and 
magnitude of errors when isokinetic conditions are not maintained. 
In one of the earlier works, Lapple and Shepherd (4) studied the 
trajectories of particles in a flow stream and presented a formula 
for estimating the order of the magnitude of errors resulting when 
there is a difference between the average sampling velocity and the 
local free stream velocity. Watson (5) examined errors in the aniso- 
kinetic sampling of spherical particles of 4 and 32 ym mass mean 
diameter (MMD) and found the relationships shown in Figure 5. Super- 
isokinetic sampling (sampling with nozzle velocity greater than the 
free stream velocity) leads to a concentration less than the actual 
concentration, while subisokinetic sampling has the opposite effect. 
Watson found that the magnitude of the error was not only a function 
of particle size as seen in Figure 5, but also of the velocity and the 
nozzle diameter. He proposed that the sampling efficiency was a function 
of the dimensionless particle inertial parameter K (Stokes number) 
defined as 

tV 

K = Cp V D -^/ISpD. = — ^ ,,, 

P o p ' ' 1 D. C3) 



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C - Cunningham correction for slippage 



p = particle density 

T = p CD -/18n 

P P ^ C4} 

P = viscosity of gas 
D^ = nozzle diameter 

The relaxation time is defined as r; it represents how quickly a particle 
can change directions. Watson concluded that to obtain a concentration 
correct within 10%. the velocity ratio R must lie between 0.86 and 1.13 
for the 32 micron particles and between 0.5 and 2.0 for the 4 micron 
particles. 

Data obtained by Dennis et al . (6] on a suspension of Cottrell 
precipitated fly ash. 14 |^i MMD, showed only a 10% negative error in 
calculated concentration for sampling velocities 60% greater than isc 
kinetic. Tests run on an atmospheric dust of 0.5 ym MMD produced no 
detectable concentration changes even while sampling at a 400% variatic 
from isokinetic flow, thus indicating that isokinetic sampling is 
relatively unimportant for fine particles. Hemeon and Haines (7) 
measured errors due to the anisokinetic sampling of particles in three 
size ranges (5-25, 80-100, and 400-500 ym) and in a range of nozzle to 
stack velocities of 0.2 to 2.0. They found that where the velocity 
ratio R ranges from 0.6 to 2.0 the extreme potential error was ap- 
proximately 50%, and that deficient nozzle velocities resulted m greater 
errors than excessive nozzle velocities. In addition, they found that 
for the coarse particles, the velocity into the nozzle had no important 



30- 



Lon 



bearing on the quantity of dust collected. They suggested using the 
product of the nozzle area and the stack gas velocity approaching the 
nozzle as the gas sample volume, regardless of the velocity of the 
nozzle. By using this method for particles greater than 80 ym, it 
is possible to obtain small deviations even where departure from 
isokinetic velocity is quite large. HTHteleyand Reed (8) also observed 
that calculating the dust concentrations from the approach velocity 
instead of the actual sampling rate produced only slight errors when 
sampling anisokinetically for large particles. 

Lundgren and Calvert (9) found the sampling bias or aspiration 
coefficient A, to be a function of the inertial impaction parameter K 
and the velocity ratio R. They developed a chart which can be used 
to predict inlet anisokinetic sampling bias depending on both K and R. 
Badzioch's CIO) equations defined the dependence of the efficiency upon 
particle inertia and the velocity ratio. In a slightly different 
terminology 



C5) 



(6} 



A = C./C^ = 1 . (R-i) g^K) 

where g(K) is a function of inertia given by 

3CK) = [1-exp C-L/£)]/(L/£) 

Z is the stopping distance or the distance a particle with initial 
velocity V^ will travel into a still fluid before coming to rest and 
is defined by [11] 

£ = TV .7. 

o (7) 



14 



L is the distance upstream from the nozzle where the flow is undisturbed 
by the do^stream nozzle. It is a function of the nozzle diameter and 
is given by the equation: 



L = nD. ^g^ 



It was observed that n lies between 5.2 and 6.8 (10). 

Flash illumination photographic techniques were used by Belyaev and 
Levin (12) to study particle aspiration. Photographic observations 
enabled them to verify Badzioch's claim that L, the undisturbed distance 
upstream of the nozzle, was between 5 to 6 times the diameter of the 
nozzle. They examined the data of previous studies on error due to 
anisokinetic sampling and concluded that the discrepancy between experi- ■ 
mental data was due to the researchers failing to take into account 
three things: 1) particle deposition in the inlet channel of the sampling 
device; 2) rebound of particles from the front edge of the sampling noz- 
zle and their subsequent aspiration into the nozzle.; and 3) the shape and 
wall thickness of the nozzle. They also found that the sampling efficiency 
was a function of the inner diameter of the nozzle, D., as well as K and R. 

In a more recent article, Belyaev and Levin (13) examined the 
dependence of the function 6CK), in equation (4), on both the inertial 
impaction parameter. K, and the velocity ratio, R. Previous authors (10, 
14) had concluded that 6(K) was a function of K alone, but Belyaev and 
Levin obtained experimental data demonstrating that for thin-walled 
nozzles, B(K) was also a function of R. Equations were developed from 
the data for values of K between O.IS and 6.0 and for values of R betv 



tween 



15 



0.16 and 5.5 



3(K,R) = 1 - 1/(1 +bK3 (9) 



where 



b = 2 + 0.617/R (10) 

Figure 6 shows a plot of equations (5) , (9) and (10] for a range of 
velocity ratios and Stokes numbers. The most significant changes in 
the aspiration coefficient occur at values of K between and 1. 
Beyond K = 1, the aspiration coefficient tends to assymptotically ap- 
proach its theoretical limit of R. Beyond a Stokes number of about 
6, it can be assumed that the aspiration coefficient equals R. This 
can be predicted both from equations (5) , (9) and (10) and from 
theoretical considerations. Badzioch (10) and Belyaev and Levin (12) 
have shown that the streamlines start to diverge at approximately 6 
diameters upstream of the nozzle. Therefore, a particle traveling at 
a velocity, V will have to change directions in an amount of time 
equal to 6D-/V . If a particle cannot change direction in this amount 
of time, it will not be able to make the turn with the streamline. 
Since T represents the amount of time required for a particle to change 
directions, setting t = 6D./V represents the limiting size particle 

10^ c 1 

that will be able to make a turn with its streamline. Rearranging these 



o o 



terms it can be seen that this situation occurs when tV /D. = 6 or at a 

o 1 

Stokes number of 6. 

Martone (15) further confirmed the importance considering free 
stream velocity as well as particle diameter when sampling aerosols by 



16 




H o o o o 



LO 

o 



o 



n 
o 



o 



17 



analyzing concentration errors obtained while sampling submicron 
particles, 0.8 m NMD and 1.28 geometric standard deviation, travel.-n. 
at near sonic and supersonic velocities. He obtained sample con- 
centrations 2-3 times greater than the true concentration when the 
sampling velocity was 205„ of the free stream velocity CR=5) . 

Sehmel (16) studied the isokinetic sampling of monodisperse 
particles in a 2.81 inch IDduct and found that it is possible to obtain 
a 20% concentration bias while sampling isokinetically with a small 
diameter inlet probe. Results also showed that for all anisokinetic 
sampling velocities, the concentration ratios were not simply cor- 
related with Stokes number. 



^-^— ^^^^^2liilg_Ji^.lJHie toN Misali 



gnment 



Sampling error associated with the nozzle misalignment has not 
been adequately evaluated in past studies because the sampled flow 
field was maintained or assumed constant in velocity and parallel to 
the duct axis. The studies that have been performed on the effect of 
probe misalignment do not provide enough quantitative information to 
understand more than just the basi.c nature of the problem. Results 
were produced through investigations by Mayhood and Langstroth, as 
reported by IVatson (5), on the effect of misalignment on the collectxor 
efficiency of 4, 12 and 37 ym particles (see Figure 7). In a study by 
Glauberman (17) on the directional dependence of air samplers, it was 
found that a sampler head facing xnto the directional air stream col- 
lected the highest concentration. Although these results coincide with 



*r- 

u 



< 
IX 






o 
u 




12 ym 



30 60 90 120 
ANGLE OF PROBE MISALIGNMENT, degrees 



Figure 7. Error due to misalignment of probe to flow stream faft 
Mayhood and Langstroth, in Watson (5]]. 



er 



19 



theoretical predictions [i.e., measured concentration is less than or 
equal to actual concentration and the concentration ratios decrease as 
the particle size and the angle are increased), the data are of little 
use since two important parameters, free stream velocity and nozzle 
diameter, are not included in the analysis. 

Raynor (18) sampled particles of 0.68, 6 and 20 ym diameter at 
wind speeds of 100, 200, 400 and 700 cm/sec with the nozzle aligned 
over a range of angles from 60 to 120 degrees. He then used a trigono- 
metric function to convert equation (5) to the form 

A = 1 + BCK)[(V.sin0 + V cos0)/ (V. cos0 + V sinG) - 1] (11) 

This function only serves to invert the velocity ratio between and 
90 degrees and does not realistically represent the physical properties 
of the flow stream. In fact, equation (11) becomes unity at 45 degrees 
regardless of what the velocity ratio or particle size is. This cannot 
be true since it has been shown that the concentration ratio will be less 
than unity and will decrease inversely proportional to the angle and 
particle diameter. 

A more representative function can be derived in the following 
manner: Consider the sampling velocity V. to be greater than the stack 
velocity V^. Let A^ be the cross sectional area of the nozzle of diameter 
D^. The stream tube approaching the nozzle will have a cross sectional 

area A such that 
o 

A V = A. V. (^7^ 

11 '-^^J 



i-(l,_*l i- '"rliil^l.t.ll- 



20 



If the nozzle is at an angle 9 to the flow streaip,, the projected area 

perpendicular to the flow is an ellipse with a major axis D., minor 

axis D.COS0, and area (D. "^cose)/4 . The projected area of the nozzle 

would therefore be A.cos0 (see Figure 8). It can be seen that all the 

particles contained in the volume V^A.cosG will enter the nozzle. A 

fraction 8'CK,R,9} of the particles in the volume (A - A.cosGlV will 

o 1 ^ o 

leave the stream tube because of their inertia and will not enter the 
nozzle. Therefore, with C^ defining the actual concentration of the 
particles, the measured concentration in the nozzle would be 

C A coseV + [l-3'(K,R,e3](A -A.cos0)V C 

C. = -5-i .JL— _ ■ _ 1 ' o o ,^^_ 

1 ~ — — (1^) 

A.V. 
1 1 

Using equations (1) and (12), this may be simplified to 

A = C^/C^ = 1 + 3'(K,R,e)(Rcos0-l) (14) 

6'(K,R,0) would be a function of both the velocity ratio R and the 
inertial impaction parameter K as shown by Belyaev and Levin (13). 
However, 3' will also be a function of the angle because as the angle 
increases, the severity of the turn that the particles must make to be 
collected is also increased. 

It can be seen that for large values of Stokes number, 6' must ap- 
proach 1 for the predicted concentration ratio in equation (14) to reach 
the theoretical limit of RcosO. The maximum error should theoretically 
occur somewhere between a Stokes number of 1 and 6 depending on the angle 
a. The upper limit of K - 6 would be for an angle of degrees as des- 
cribed earlier in this chapter. The theoretical lower limit of K = 1 



1 1 miatim^ m^ nt^czmaai^uUii:.^^^^ 



21 





>s 



o 
o 



> 






Pi 
m 



+-> 

0) 

c 

■r-< 
O 

•H 

c 

nj 

•n 
(=; 



• H 
1— I 
cd 
i/i 

•H 

e 

CD 
I— I 
N 
N 
O 

c 



•H 






CO 

0) 



22 



would be for an angle o£ 90 degrees in which case the particles would 
be traveling perpendicular to the nozzle. Since the nozzle has zero 
frontal area relative to the flow stream, any particle that is collected 
must make a turn into the nozzle. The amount of time that a particle 
has to negotiate a turn is the time it takes the particle to traverse 
the diameter of the nozzle, or D^/V . Setting this equal to T the time 
it takes a particle to change directions and rearranging terms, we ob- 
tain tV^/D^ = 1 as the limiting situation for a particle to be able to 
make a turn into a nozzle positioned at a 90 degree angle to the flow 
stream. For angles between and 90 degrees the maximum error will 
occur between the limits of Stokes numbers of 1 and 6 and should be 
proportional to the average diameter of the frontal area of the nozzle. 
Fuchs [19) suggests that for small angles the sampling efficiency will 
be of the form 

A = 1 - 4 sinCGK/TT) (15) 

Laktionov (20) sampled a polydisperse oil aerosol at an angle to 
the flow stream of 90 degrees for three subisokinetic conditions. He 
used a photoelectric installation to enable him to determine the aspira- 
tion coefficients for different sized particles. From data obtained 
over a range of Stokes numbers from 0.003 to 0.2 he developed the fol- 
lowing empirical equation: 

, ^ .,.[v./v )°'^ 

A = 1 - jK^ i' 0-' (16) 

This equation can be used only in the range of Stokes numbers given and 
for a range in velocity ratios (R) from 1.25 to 6.25. 



23 



A few analytical studies in this area have also been published. 
Davies' (14) theoretical calculations of particle trajectories in a 
nonviscous flow into a point sink determined the sampling accuracy 
to be a function of the nozzle inlet orientation and diameter, the 
sampling flow rate and the dust particle inertia. Vitols (21) also 
made theoretical estimates of errors due to anisokinetic sampling. 
He used a procedure combining an analog and a digital computer and 
considered inertia as the predominant mechanism in the collection of 
the particulate matter. However, the results obtained by Vitols are 
only for high values of Stokes numbers and are of little value for 
this study. 



B. Summary of the Literature on Tangential Fl 



ow 



Although anisokinetic sampling velocity is known to cause a 
particle sampling bias or error, there are also several other sampling 
error-causing factors such as: duct turbulence; external force fields 
(e.g., centrifugal, electrical, gravitational or thermal); and probe 
misalignment due to tangential or circulation flow. These factors are 
almost always present in an industrial stack gas and cannot be assumed 
to be negligible. Not only do these factors cause sampling error 
directly but in addition, they cause particulate concentration gradients 
and aerosol size distribution variations to exist across the stack - 
both in the radial and angular directions. 



1. Causes and Characteristics_ of Tangential Fl 



oiv 



an 



Tangential flow is the non-random flow in a direction other th 
that parallel to the duct center line direction. In an air pollution 



24 



control device, whenever centrifugal force is used as the primary 
particle collecting mechanism, tangential flow will occur. Gas 
flowing from the outlet of a cyclone is a classic example of tangential 
flow and a well recognized problem area for accurate particulate sampling. 
Tangential flow can also be caused by flow changes induced by ducting 
(22). If the duct work introduces the gas stream into the stack 
tangentially, a helical flow will occur (see Figure 9). Even if the 
flow stream enters the center of the stack, if the ducting flow rate is 
within an order of magnitude of the stack flow rate, a double vortex 
flow pattern will occur (see Figure 10) . 

The swirling flow in the stack combines the characteristics of 
vortex motion with axial motion along the stack axis. The gas stream 
moves in spiral or helical paths up the stack. Since this represents 
a developing flow field, the swirl level decays and the velocity pro- 
files and static pressure distributions change with axial position 
along the stack. Swirl level is used here to represent the axial flow 
or transport rate of angular momentum (23) . Velocity vectors in 
tangential or vortex flows are composed of axial, radial and tangential 
or circumferential velocity components (see Figure 11). The established 
vortex flows are generally axisymmetric but during formation of the 
spiraling flow the symmetry is often distorted. The relative order of 
magnitude of the velocity components varies across the flow field with 
the possibLlity of each one of the components becoming dominant at 
particular points (24) . 



-^■Wii^^diir^ ■■ 



25 




< 
a. 

o 




c 

•H 
+J 

o 

U 
3 

C 
>H 

s 
o 

i-i 



■H 
+J 

faO 
C 



CD 

■H 



26 




m 
< 

I 



tc 



+-> 
o 

3 
T3 

X 

o 

c 

•H 

o 

X 

u 

o 
> 



3 

a 



o 

M 



M 
3 

•H 






27 





Figure 11. Velocity components in a swirling flow field. 



28 



The two distinctly different types of flow that are possible in 
a swirling flow field are knovm as free vortex and forced vortex flows. 
When the swirling component of flow is first created in the cyclone 
exit, the tangential profile of the induced flow approaches that of a 
forced vortex. As the forced vortex flow moves along the axis of the 
stack, momentum transfer and losses occur at the wall which cause a 
reduction in the tangential velocity and dissipation of angular 
momentum. This loss of angular momentum is due to viscous action 
aided by unstable flow and fluctuating components. Simultaneously, 
outside the laminar sublayer at the wall where inertial forces are 
significant, the field develops toward a state of constant angular 
momentum. This type of flow field with constant angular momention 
is classified as free vortex flow. The angular momentum and tangential 
velocities of the flow decay as the gas stream flows up the stack (23) . 

Baker and Sayre measured axial and tangential point velocity 
distributions in a 14.6 cm circular duct in which swirling flow was 
produced by fixed vanes (23) . The tangential velocity profiles and 
angular momentum distributions are plotted in Figures 12 and 13 from 
measurements taken at 9, 24 and 44 diameters downstream of the origin 
of tangential flow. The tangential velocity (W) is made dimensionless 
by dividing it by the mean spatial axial velocity (U^) at a pipe cross 
section. These plots indicate developing flow fields, with two definite 
types of flow occurring: that approaching forced vortex flow in the 
central region of the pipe and flow approaching free vortex flow in 
the outer region. Further tests showed that the free vortex field 



29 




rH 

CD 

•H 

Mh 

a 

o 
.-( 



m 



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> 



• H 
■)-> 

c 

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c« 
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o 

PJ 
o 

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U 
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•rt 
13 



R 
O 

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+J 

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d) 

U3 

tn 
o 

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So 

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30 



1 


i 1 1 


1 ' ' 




r— 

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f 


1 





- \ 




-1- \ 
r-i \ 


II 






- 


«• 


/ 

11 

X 


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\ 


\ 
\ 




_ 


-' 






\\ 


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- 


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^ 


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development is due primarily to viscosity at the wall and not a function 
of inlet conditions, whereas the profiles in the forced vortex field are 
very dependent on the initial conditions at the inlet. Although no re- 
verse flow was found in these tests, other tests showed that strong 
swirls may produce reversed axial velocities in the central region (25) . 

It should be noted that although tangential velocities and angular 
momentum decay along the axis of the pipe, see Figures 12 and 13, even 
after 44 diameter the tangential velocity is still quite significant 
when compared to the axial velocity. Therefore, satisfying the EPA 
Method 5 requirement of sampling 8 stack diameters downstream of the 
nearest upstream disturbances will not eliminate the effect of sampling 
in tangential flow. 

The angle of the flow relative to the axis of the stack induced by 
the tangential component of velocity was as high as 60 degrees at some 
points in the flow. This compares well with angles found when sampling 
the outlets of cyclones (25) . Another interesting fact about the flow 
described in Figures 12 and 13 is that the radial positions for the 
tangential components W/U = show that the vortex axis is off center 
by as much as O.lr/R. This indicates that the swirling fields are not 
exactly axis^-mmetrical . 

2. Errors Induced by Tangential Flow 

Types of errors that would be expected to be introduced by tangential 
flow are nozzle misalignment, concentration gradients and invalid flow 
measurements. The sampling error caused by nozzle misalignment lias been 



32 



described in the previous chapter. Concentration gradients occur 
because the rotational flow in the stack acts somewhat as a cyclone. 
The centrifugal force causes the larger particles to move toward the 
walls of the stack, causing higher concentrations in the outer regions. 

Mason (22] ran tests at the outlet of a small industrial cyclone 
to determine the magnitude of these three types of errors induced by 
cyclonic flow. Results of flow rates determined at the different 
locations are presented in Table I. As indicated by the data, serious 
errors can result in cases of tangential flow. A maximum error of 212°', 
occurred when the pitot tube was rotated to read a maximum velocity 
head. Sampling parallel to the stack wall also had a large error of 
almost 74-6. When sampling downstream of the flow straightening vanes, 
however, the error was reduced to 15%. 

Tests performed at the same point but with different nozzle 
angles produced the data in Table 11. Measured dust concentration 
was lowest when the sampling nozzle was located at an angle of degrees 
or parallel to the stack wall. The measured dust concentration con- 
tinued to increase at 30 and 60 degrees but then decreased at 90 degrees. 
Equation (14) shoivs that when sampling at an angle, under apparent iso- 
kinetic conditions (i.e., R=l) , the measured concentration will be less 
than the true concentration by a factor directly proportional to the 
cos9. A maximum concentration, which would be the true concentration, 
will occur at = 0, which from this data should lie at an angle between 
60 and 90 degrees to the axis of the stack. This can be confirmed by 



vs»ss>»"- i^S^L^i^^fi^^s^ 2i''\'i.*.^r>^.^ 



TABLE I 
FLOW RATE DETERMINED AT VARIOUS MEASURENENT LOCATIONS 



Location 



VelocjLty_j;fp_sJ__ Flow Rate (scfm) % Error 



Actual Based on 
Fan Performance 

Port A 
(parallel) 

Port A 
(maximum Ap) 

Port C 
(straightened) 



18 



40 



60 



21 



475 



826 



1,482 



548 



74 



212 



15 



34 



TABLE II 
CONCENTRATION AT A POINT FOR DIFFERENT SAMPLING ANGLES 



Nozzle Angle 


30 
60 
90 



easured Concentration 


(grains/dscf) 





243 





296 





332 





316 



n ,..4«4 <c « .» •k^M » ■ 



35 



using the data in Table I and the geometry in Figure 11 to calculate 
the angle cj): 

cos(|) = V /V = 18/60 (17) 

This is true for ^ - 12 degrees. Therefore, 9 = when (}) = 72 degrees. 

:| Table III gives the results of the emission tests. Sampling with 

I 

il the nozzle parallel to the stack wall showed an error of 53%. 

I 

j Sampling at the angle of maximum velocity head reduced the error 

to 40-<;. The results cannot be compared directly to those with the 
parallel sampling approach because the feed rates were not the same 
due to equipment failure and replacement. Sampling in the straightened 
flow had a sampling error of 36%. It was expected that sampling at this 
location would give better results, but some of the particles were im- 
pacted on the straightening vanes and settled in the horizontal section 
of the duct, thus removing them from the flow stream. 

Particle size distribution tests showed no significant effect of 
a concentration gradient across the traverse. This was due to the 
particles being too small to be affected by the centrifugal force field 
set up by the rotating flow. 



5. Errors Due to t he S-Type Pitot Tube 

The errors in the measurement of velocity and subsequent calculations 
of flow rate in tangential flow are due primarily to the crudenoss of the 
instruments used in source sampling. Because of the high particulate 
loadings that exist in source sampling, standard pitot tubes cannot be 
used to measure the velocity. Instead, the S-type pitot tube must be used 



TABLE III 
EMISSION TEST RESULTS 



Probe Position 



Measured Emission 
Rate (gr/dscf) 



Actual Emission 
Rate (gr/dscf) 



Error % 



Nozzle parallel 
with stack wall 

Nozzle rotated 
toward maximum Ap 

Straightened flow 



0.350 

0.194 
0.207 



0.752 



53 



0.327 40 

0.325 36 



37 



since it has large diameter pressure ports that will not plug (see 
Figure 14) . Besides the large pressure ports it has an additional 
advantage of producing approximately a 20% higher differential pressure 
than the standard pitot tube for a given velocity. However, although 
the S-type pitot tube will give an accurate velocity measurement, it is 
somewhat insensitive to the direction of the flow (25-29) . Figures 15 
and 16 show the velocity errors for yaw and pitch angles. Although the 
S-type pitot tube is very sensitive to pitch direction, the curve for 
yaw angle is symmetrical and somewhat flat for an angle of 45 degrees 
in either direction. Because of this insensitivity to direction of flow 
in the yaw direction, the S-type pitot tube cannot be used in a tangential 
flow situation to align the nozzle to the direction of the flow, or to 
accurately measure the velocity in a particular direction. 

The velocity in a rotational flow field can be broken up into three 
components in the axial, radial and tangential directions (see Figure 11). 
The magnitude of the radial and tangential components relative to the 
axial component will determine the degree of error induced by the tangential 
flow. Neither the radial nor the tangential components of velocity affect 
the flow rate through the stack, but both affect the velocity measurement 
made by the S-type pitot tube because it lacks directional sensitivity. 
If the maximum velocity head were used to calculate the stack velocity, 
the resultant calculated flow rates and emission levels could be off by 
as much as a factor of l/cos(J). Aligning the probe parallel to the stack 
will reduce but not eliminate this error because part of the radial and 
tangential velocity components will still be detected by the pitot tube. 



38 




•i-r 
«4-i 



in 

I — f 

c 









■p 
o 



o 
1:1- 

I 






39 




00 

o 

D 



•H 



C- 



c 

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a; 
> 



U 
no 



40 




a 


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E 


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to 


O) 


o 


□ 



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41 



L 



Therefore, the true flow rate cannot be determined by an S-type pitot 
tube in tangential flow because neither the radial velocitv, V , the 
tangential velocity, V the axial velocity, V , nor the angle c^ can 
be measured directly. 



ii-JMlH^^^A^i^ilable^Jo^^ in a Tangential 
Flow Field ~^"" "~ ~ — -^_ ^^ — _ 



Almost all of the reported measurements of velocity components in 
a tangential flow field have been based upon introduction of probes into 
the flow. Because of the sensitivity of vortex flows to the introduction 
of probes, the probe dimensions must be small with respect to the vortex 
core in order to accurately measure velocity. 

Two common types of pressure probes capable of measuring velocity 
accurately are the 5-hole and 5-holc pitot tubes pictured in Figures 17a 
and b. The 5-hole or three dimensional directional pressure probe is 
used to measure yaw and pitch angles, and total and static pressure. 
Five pressure taps are drilled in a hemispherical or conical probe tip, 
one on the axis and at the pole of the tip, the other four spaced 
equidistant from the first and from each other at an angle of 30 to 50 
degrees from the pole. The operation of the probe is based upon the 
surface pressure distribution around the probe tip. If the probe is 
placed in a flow field at an angle to the total mean velocity vector, 
then a pressure differential will be set up across these holes; the 
magnitude of which will depend upon the geometry of the probe tip, 
relative position of the holes and the magnitude and direction of the 
velocity vector. Each probe requires calibration of the pressure 



42 




_J 




o 



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O 

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■^•^^-Tl**»-»«<V. 



ailBj .t«. !£-■■■■■=» 



45 



differentials betvveen holes as a function of yaw and pitch angles. 
Figure IS shows the sensitivity of a typical 5-hole pitot tube to yaw 
angle. Because of its sensitivity to yaw angle, it is possible to rotate 
the probe until the yaw pressures are equal, measure the angle of probe 
rotation (yaw angle) and then determine the pitch angle from the re- 
maining pressure differentials. The probe can be used without rotation 
by using the complete set of calibration curves but the complexity of 
measurement and calculation is increased and accuracy is reduced. Vel- 
ocity components can then be calculated from the measured total pressure, 
static pressure and yaw and pitch angle measurements. 

The 3-hole pitot tube, also known as the two dimensional or 
Fecheimer probe, is similar to the 5-hole design except that it is 
unable to measure pitch angle. The probe is characterized by a central 
total pressure opening at the tip of the probe with two static pressure 
taps placed s>imiietrically to the side at an angle of from 20 to 50 
degrees. From Figure 19 it can be seen that the probe is quite sensitive 
to yaw angle and can therefore be used to determine the yaw angle by 
rotating the probe until the pressure readings at the static taps are 
equal. Once this is done the total pressure is read from the central 
port, and the static pressure can be determined by use of a calibration 
chart for the particular probe. Both the 5-hole and the 3-hole pitot 
tubes have proven useful in determination of velocity components in 
tangential flow fields (25, 28, 30). 



5. EPA Criteria for Sampling _Cyc lonic Fl 



ow 



The revisions to reference methods 1-8 (2) describe a test for 
determination of whether cyclonic flow exists in a stack. The S-type 



sMitim**r-,mf.i 



44 




Figure 18. ('ive-holc pi 



pitot tube sensitivity to yaw angle. (281 



45 




■30 -25 -20 -15 -10 -5 




5 10 15 20 25 30 
Pitch Angle, degrees 
.05 



.10 
Pressure 
Differential , 
inches of f!^0 

- -.15 



Figure 19. Fcchcimcr pitot tube sensitivity to yaw angle. (28) 



■S*M $ ■(.« •*- - 



" v^,i)r"*^*.«««-'s.i»-*>*t*"- 



i«-r»'**«. - i| > i I—— ,mi,»-«t.^—t 



46 



pitot tube is used to determine the angle of the flow relative to the 
axis of the stack by turning the pitot tube until the pressure reading 
at the two pressure openings is the same. If the average angle of the 
flow across the cross section of the stack is greater then 10 degrees, 
then an alternative method of Method 5 should be used to sample the 
gas stream. The alternative procedures include installation of 
straightening vanes, calculating the total volumetric flow rate 
stoichiometrically, or moving to another measurement site at which the 
flow is acceptable. 

Straightening vanes have shown the capability of reducing swirling 
flows; however, there are some problems inherent in their use. One is 
the physical limitation of placing them in an existing stack. Another 
is the cost in terms of energy due to the loss of velocity pressure 
when eliminating the tangential and radial components of velocity. 
Since the vortex flows are so sensitive to downstream disturbances, 
it is quite possible that straightening vanes might have a drastic 
effect on the performance of the upstream cyclonic control device 
which is generating the tangential flow. Because of these reasons the 
use of straightening vanes is unacceptable in many situations. 

Calculating the volumetric flow rate stoichiometrically might 
produce accurate flow rates but the values could not be used to 
calculate the necessary isokinetic sampling velocities and directions. 
Also, studies reported here have shown that the decay of the tangential 
component of velocity in circular stacks is rather slow and therefore 
it would be unlikely that another measurement site would solve the problem. 



47 



It should be noted that EPA's approach to determining whctlier 
cyclonic flow exists in a stack is correct. Other approaches such 
as observing the behavior of the plume after leaving the stack could 
lead to improper conclusions. Hanson et al (28} found that the 
twin-spiraling vorticies often seen leaving stacks are the result of 
secondary flow effects generated by the bending of the gas stream by 
the prevailing crosswind and do not indicate any cyclonic flow 
existing in the stack. 



CHAPTER III 
EXPERIMENTAL APPARATUS AND METHODS 



A. Experimental Design 



The major components of the aerosol flow system can be seen in 
Figure 20. An aerosol stream generated from a spinning disc generator 
was fed into a mixing chamber where it was combined with dilution air. 
The air stream then flowed through a 10 cm diameter PVC pipe containing 
straightening vanes. This was followed by a straight section of clear 
pipe from which samples were taken. The filter holder and nozzle used 
as a control sample originated in a box following the straight section. 
A test nozzle was inserted into the duct at an angle from outside the 
box. A thin-plate orifice, used to monitor flow rate, followed the 
sampling box. A 34000 £pm industrial blower was used to move the air 
through the system. The flow rate could be controlled by changing the 
diameter of an orifice plate. An air by-pass between the blower and 
the orifice plate was used as a fine adjust for the flow. 

The sampling systems (see Figure 21] consisted of stainless steel, 
thin-walled nozzles connected to 47 mm stainless steel Gelman filter 
holders. Each filter assembly was connected in series to a dry gas 
meter and a rotameter, and driven by an airtight pump with a by-pass 
valve to control flow. 



48 



49 



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•rH 

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51 



B^ Aeroso l Generation 
1_^ Sj^in ning Disc Generator 

A spinning disc aerosol generator (51-33) was used to generate 
monodisperse aerosols from 1.0 ym NMD to 11.1 ym NMD [see Table IV). 
Droplets were generated from a mixture of 90% uranine (a fluorescent 
dye) and 10?6 methylene blue dissolved in a solution of from 90 to 100% 
ethanol (95% pure) and up to 10% distil led/deionized H^O. Uranine was 
used so that the particles could be detected by fluoremetric methods. 
Methylene blue was added to aid in the optical sizing of the particles. 
The mixture of water and ethanol allowed for a uniform evaporation of the 
droplets. The droplets, containing dissolved solute, evaporated to yield 
particles whose diameters could be calculated from the equation 



% = ^^'-''^ % (IB) 



where 



D = particle diameter, ym 

C^ = ratio of solute volume to solvent volume plus solute 

volume, dimensionless 
Dp = original droplet diameter, ym 

With the disc's rotational velocity, air flows and liquid feed rate held 
constant the size of the droplets produced were only dependent upon the 
ratio of the ethanol -water mixture. Since the droplets are produced from 
a dynamic force balance between the centrifugal force and the surface 



52 



TABLE IV 
SIZES AND DESCRIPTIONS OF EXPERIMENTAL AEROSOLS 



Aerosol 
Description 


Generation 
Method 


% 

Ethan 


0.0024% 


Spinning Disc 


90 


0.005% 


Spinning Disc 


90 


0.01% 


Spinning Disc 


90 


0.03% 


Spinning Disc 


90 


0.2% 


Spinning Disc 


99 


0.05% 


Spinning Disc 


90 


0.55% 


Spinning Disc 


99 


0.3% 


Spinning Disc 


90 


0.6% 


Spinning Disc 


90 


2.0% 


Spinning Disc 


100 


1.0% 


Spinning Disc 


90 


4.0% 


Spinning Disc 


100 


6.7% 


Spinning Disc 


100 


6.7% 


Spinning Disc 


95 


lagweed 
Pollen 


Mechanical 
Dispersion 


N.A. 



Number Mean 
Droplet Diameter 



Ethanol Diameter, pm Particles, 



37 


.4 


37 


.2 


37 


.1 


37 


.8 


24 


.6 


39 


.7 


24 


.4 


34. 


,5 


33. 


,1 


23. 


6 


35. 


4 


23. 


4 


23. 


2 


27. 


3 



pm 



1 


.08 


1 


.37 


1, 


.72 


2. 


,53 


3. 


10 


3. 


15 



4.98 
6.02 
6.4 
7.66 
8.0 
9.42 
11.1 

N.A. 19.9 



55 



tension of the drop, the surface characteristics of the liquid are 
quite important. The surface tensions of water and ethanol at 20 
degrees C are respectively 72.8 and 22.3 dynes/cm (34). The effect 
of this large difference can be seen in Table IV where the droplets 
produced were approximately 37 ym for 90% ethanol and 23 ym for 100% 
ethanol . 

Before and after each test a sample of the particles was collected 
on a membrane filter and sized using a light microscope to take into 
account any slight variation in the performance of the spinning disc. 

2. Ragweed Pollen 

In order to obtain large Stokes numbers, ragweed pollen was 
mechanically dispersed by means of a rubber squeeze bulb into the 
inlet of the duct. The ragweed pollen had a NMD of 19.9 ym. 

C. Velocity Determination 

The velocity at each sampling point was measured using a standard 
pitot tube. The flow was maintained constant during the test by con- 
trolling the pressure drop across a thin-walled orifice placed in the 
system (35-37). Five orifice plates with orifices ranging in diameter 
from 1.8 to 7.2 cm were used to obtain a range in duct velocities of 
82 to 2460 cm/sec (see Table V) in the 10 cm duct. To obtain higher 
velocities, a 5 cm duct was used. 

A typical velocity profile across the 9 . 6 cm clear plastic duct 
is presented in Table VI and plotted in Figure 22. The profile is 



■ (m'-: ■■lllllir"-- ■.ill*"**=« w^ * *-"^.M » 



54 



TABLE V 
TABLE OF OBTAINABLE VELOCITIES IN 10 cm DUCT 



Orii 


-ice Diameter 


Ap Range 


Ran 


ge in 


Velocity 




cm 


cm H^b 
5.6 - 21.6 




cm/ 


sec 




1 . 795 




82 


- 162 




2.539 


5.3 - 21.8 




162 


- 326 




5.5 89 


4.2 - 22.9 




304 


- 670 




5.080 


4.1 - 22.6 




582 


- 1371 




7.182 


2.2 - 14.5 




945 


- 2460 



55 



TABLE VI 
TYPICAL VELOCITY TRAVERSE IN THE EXPERIMENTAL SMIPLING SYSTEM 

(9.58 cm I.D. Duct) 



Point 


d/D 


AP 


Hor 

, cm 11^ 


■izontal 

V, cm/sec 


AP, cm 


Vert 


ical 

V 


, cm/ sec 


1 


0.044 




1.27 




1454 


1.57 






161S 


2 


. 146 




1.83 




1743 


2.11 






1871 


3 


0.296 




2.03 




1S3S 


2. OS 






1859 


4 


0.704 




2.13 




1884 


2.11 






1871 


5 


. 854 




1.88 




1768 


1.98 






1813 


6 


0.956 




1.47 




1564 


1.52 






1591 



Average Velocities [cm/sec) 

From Pitot Tube Readings From Orifice AP 

1740 1658 






56 




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57 



quite flat which is typical of the turbulent flow regime. The average 
Reynolds number for this particular case was 1.1 x 10 . The velocities 
at traverse points 3 and 4 were used as the velocity for determination 
of isokinetic sampling rate and Stokes number. The difference between 
the average velocity determined from the pitot traverse and the orifice 
plate calibration is probably due to the inability of the pitot tube to 
accurately measure velocity near the wall at points 1 and 6. 

D. Selection of Sampling Locations 

Sehmel (16) observed that non-uniform particle concentrations 
existed across the diameter of a cylindrical duct, and that the 
magnitude of the concentration gradient varied with particle size. 
To account for these radial variations, the two sampling points were 
located symmetrically about the center of the duct at a distance of 
2 cm from the center. Simultaneous isokinetic samples were taken at 
the two points and compared. Tests were repeated for different 
particle sizes. No concentration differences were found to exist at 
the two sampling points. 

E. Sampling Nozzles 

Two pairs of sampling nozzles were cut from stainless steel tubing 
of 0.465 cm and 0.683 cm l.D. The nozzles were made approximately 15 cm 
long to minimize the effect of the disturbance caused by the filter 
holders on the flow at the entrance of the nozzles. Analysis by Smith 
(38) showed that a sharp-edge probe was the most efficient design; 



it!:*A4-.*^it*— iC-ii^-t -NS-Ui - i<i>.»r«r:;w 



58 



therefore, the tubing was tapered on a lathe to a fine edge. Belyaev 
and Levin (12) observed that the rebound of particles from the tip of 
the nozzle into the probe was one cause of sampling error and that for 
tapered nozzles, the efficiency is affected by the relative wall thick- 
ness, the relative edge thickness and the angle of taper. They con- 
cluded that if the edge thickness is less than 5% of the internal diameter 
and the taper is less than 15 degrees, then the variation in aspiration 
coefficient due to particle rebound would be less than 5%. The nozzles 
were designed accordingly. 

F. Analysis Procedu re 

1. For Uranine Particles 

Uranine particles were collected on Gelman type A glass fiber 
filters. The filters were then placed in a 250 ml beaker. One hundred 
milliliters of distilled water were then pipetted into the front half of 
the filter holder and down through the nozzle into the beaker containing 
the filter. The uranine leachate concentration was then diluted and 
analyzed by a fluorometer (39) . 

2. For Ragweed Pollen 

The ragweed pollen was collected on membrane filters and counted 
under a stereo microscope. In this part of the experiment the filters 
and probe were analyzed separately. The filters used for collecting 
the particles were 5.0 pm type SM Millipore membrane filters. In order 
to count the particles under a microscope a dark background was necessary; 



M-**^. Vf lD«l<lnir'IMni.<T-«-~-kJJlfl>iM'1Ui-t>|«c<''^kMM 



59 



therefore, each filter was dyed with ink and a grid was drawn to aid 
in the counting. Before being placed in the filter holders, the filters 
were examined under the microscope to determine if any background count 
existed. After each test the filters were removed and the entire area 
of the filter was counted. 

The pollen caught in the nozzle and filter holder was analyzed 
using isopropyl alcohol and 0.45 ym pore size Millipore membrane filters 
with black grids. The isopropyl was first filtered several times to 
remove background particulate matter. Once the background was low enough, 
the alcohol was poured into the front half of the filter holder and 
through the nozzles. The solution was then sucked through the membrane 
filters. The filters were allowed to dry and then the entire filter 
area was counted under the microscope. 

G. Sampling Proc edure 

1. A desired flow rate was obtained by selecting an orifice 
plate and using the by-pass as a fine adjust. 

2. The velocity was measured using a standard pitot tube. 

3. A solute-solvent solution was selected for a given particle 
size. 

4. Particles were collected on a membrane filter and sized 
using a light microscope. 

5. A nozzle diameter which would allow for an isokinetic 
sampling rate closest to 1 cfm was selected. 

6. Isokinetic sampling rates were calculated and sampling 
flow rates were adjusted accordincrly . 



■■"•-id WrTTi ;>•(•.-• ♦• I 



60 



7. Two simultaneous isokinetic samples were taken, one 

parallel to the flow (control), and one at a specified 
angle. Sampling times i^aried from 10 to 20 minutes. 

H. Tangential Flow Mapping 

The system used to map the flow pattern in a tangential flow stream 
is shown in Figure 25. It consists of a 54000 £pm industrial blower, a 
section of 15 cm PVC pipe containing straightening vanes, a small in- 
dustrial cyclone collector, followed by a 6.1 meter length of 20 cm PVC 
pipe. The 150 cm long cyclone, shown in Figure 24 was laid on its side 
so that the stack was horizontal and could be conveniently traversed at 
several points along its length. A change in flow through this system 
could be produced by supplying a restriction at the inlet to the blower. 

To measure the velocity in the stack a United Sensor type DA 5- 
dimentional directional pitot tube was used. The probe, pictured with 
its traversing unit in Figure 25, is .32 cm in diameter and is capable 
of measuring yaw and pitch angles of the fluid flow as well as total 
and static pressures. From the blow up of the probe tip (Figure 25) it 
can be seen that the head consists of 5 pressure ports. Port number 1 
is the centrally located total pressure tap. On each side are two 
lateral pressure taps 2 and 3. When the probe is rotated by the manual 
traverse unit until P., = P,, the yaw angle of flow is indicated by the 
traverse unit scale. When the yaw angle has been determined an additional 
differential pressure is measured by pressure holes located perpendicularly 
above and below the total pressure hole 1. Pitch angle is then determined 
using a calibration curve for the individual probe. The yaw angle is a 



61 



]5 cm. ID 




Straightening van cs 



.4 m — 



Slower 




6.1 m 



Figure 23. 



Experimental system for measuring 
cro.^s sectional flow patterns in 
a swirling flow stream. 



3 
V) 

re 
o 



-> 



!Ocm 




I Ti^i^s-**-?' n*««w- 



62 




k-22.f 



0— > 




! 1 



T 



T 



Note: All dimensions 
in centimeters 



lI_j^J 



17.1 



14.7 




Figure 24. Cyclone used in the study to generate swirling fl 



ow. 



63 




3 1 




2 4 



Figure 25. Photograph of the 5-dimcns Lonal pitot with its 
traversing unit. Insert shows the location of 
the pressure taps. 



64 



measure o£ the flow perpendicular to the axis of the stack and tangent 
to the stack walls. The pitch angle is a measure of the flow perpendic- 
ular to the axis of the stack and perpendicular to the stack walls. The 
axial component of the velocity can therefore be determined from the 
following equation: 



V^ = V^ coscj) (19) 



where V = component of velocity flowing parallel to tlie axis of the stack, 
a 

V = total or maximum velocity measured by the pitot tube 
(j) = cos [cos (pitch) X cos (yaw)] 



CHAPTER IV 
RESULTS AND ANALYSIS 



A. Ae rosol Sampling Experiments 

1. Stokes Number 

Experiments were set up and run with Stokes number as the independent 
variable. Duct velocity, nozzle diameter and particle diameter were varied 
in order to produce a range of Stokes numbers from 0.007 to 2.97. The 
Stokes number used in the analysis of data was calculated from 

Cp V D " 

1 

where 

-fn 4^4 n /LI 
C = 1 + 2.492 L/D + 0.84 L/D e ' ' ■ p' ^ (11) (21) 

p p 



and 



L = mean free path = 0.065 pm (11) 



Values for density and viscosity used in the calculations were 
n = 1.81 X 10""^ g/cm-sec (40) 

p = density of uranine particles = 1.375 g/cm." (41) 
p = density of ragweed pollen = 1.1 g/cm (18) 



65 



66 



2 ■ Sampl J^ng with Parallel N ozzles 

In order to determine if the concentration of particles was the 
same at both sampling locations, simultaneous samples were taken with 
both nozzles aligned parallel to the duct. Table VII shows the results 
of tests performed over a range of Stokes numbers from 0.022 to 1.75. 
The average over all of the tests showed only a 0.34% difference between 
the two points with a 95% confidence interval of ±1.2%. The data show 
an increase in the range of the values as the Stokes number increases. 
This can be expected because a small error in probe misalignment would 
have a greater effect at the higher Stokes number. 

5. Analysis of Probe Wa sh 

In the analysis of the tests using ragweed pollen, the filter 
catch and probe wash were measured separately. This method allowed 
for the determination of the importance of analyzing both the filter 
and wash. From Table VIII it can be seen that even for a solid dry 
particle, analysis of the probe wash is a necessity. An average of 
40% of the particles entering the nozzle was collected on the walls of 
the nozzle-filter holder assembly. This was only for nozzles aligned 
parallel to the flow stream and sampling isokinetically . Therefore, 
the loss of particles was due to turbulent deposition and possibly 
bounce off the filter, and probably not inertial impaction. For tests 
run with the nozzle at an angle to the flow stream, it is assumed that 
the loss would increase as impaction of particles on the walls became 



67 



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TABLE VIII 
PERCENT OF PARTICULATE MATTER COLLECTED IN THE PROBE WASH 
FOR NOZZLES PARALLEL WITH THE FLOW STREAM 



68 



Probe W ash* 

511 
196 
161 
366 
407 
377 
265 
415 
351 
220 
442 



Filter" 



Totar 



497 


1008 


218 


414 


250 


411 


721 


1087 


697 


1104 


669 


1046 


464 


729 


647 


1062 


522 


873 


240 


460 


614 


1036 



-6 in Wash 

51 
47 
39 
34 
37 

36: 

36 

39 
40 
15 
41 



''Numbers represent the number of ragweed pollen counted. 



69 



important. This can be seen from the data taken at 60 degrees (see 
Table IX) where an average of 54% of the particles was lost on the 
walls . 

The probe wash for eight tests using 6.7 ym uranine particles 
was also analyzed separately for comparison with the results of the 
ragweed pollen tests. While parallel sampling, from 15 to 34% of the 
total mass was collected in the nozzle and front end of the filter 
holder. While this was somewhat less than the amount of ragweed pol- 
len found in the nozzle, it is substantial enough to show the importance 
of including the nozzle wash with the filter catch. Also because of the 
variation of the percent collected in the nozzle during identical tests, 
the probe wash cannot be accounted for by a correction factor. During 
further testing, it was qualitatively observed that the percent in the 
probe wash increased with particle size and decreased with increasing 
nozzle diameter. 

4. The Effect of Angle Misalignmen t on Sampli ng Efficiency 

The aspiration coefficient was determined by comparing the amount 
of particulate matter captured while sampling isokinetically with a 
control nozzle placed parallel and a test nozzle set at an angle to the 
flow stream. Tests were run at three angles, .30, 60 and 90 degrees. 
The results showed the theoretical predictions to be quite accurate. 
For all three angles the aspiration coefficient approached 1 for small 
Stokes numbers (K) , decreased as K increased and then leveled off at a 
minimum of cos8 for large values of Stokes number. The most significant 
changes occur in the range between K = 0.01 and K = 1.0. 



70 



TABLE IX 

PERCENT OF PARTICULATE MATTER COLLECTED IN THE PROBE WASH 

FOR NOZZLES AT AN ANGLE OF 60 DEGREES WITH THE FLOW STRE/\iM 



Probe Wash* 


Filter* 


Total* 


% in Wash 


348 


211 


559 


62.0 


161 


138 


299 


54.0 


288 


333 


621 


46.4 



Numbers represent the number of ragweed pollen counted. 



71 



Figures 26, 27 and 28 represent the sampling efficiency as a 
function of Stokes number for 30, 60 and 90 degrees respectively. 
The experimental data used in these plots are presented in Tables X, 
XI and XII. From these tables it can be seen that the variables of 
particle diameter and velocity and nozzle diameter were varied rather 
randomly. This was done to check the legitimacy of using Stokes number 
as the principle independent variable. From the shape of the curves in 
Figures 26-28, it can be seen that the aspiration coefficient is indeed 
a function primarily of Stokes number. 

The curves for 30, 60 and 90 degrees are all similar in shape 
except for the values of Stokes number where they approach their 
theoretical limit. As the angle of misalignment increases, the more 
rapidly the aspiration coefficient reaches its maximum error. This 
can be accounted for as an apparent change in nozzle diameter, because 
it is the only parameter in the Stokes number that is affected by the 
nozzle angle to the flow stream. As described before, the nozzle 
diameter is important because it determines the amount of time available 
for the particle to change directions (approximately 6 D./V ). As the 
nozzle is tilted at an angle to the flow stream, the projected frontal 
area and therefore the projected nozzle diameter are reduced proportional 
to the angle. Therefore, as the angle of misalignment increases, the 
time available for the particle to change direction decreases leading to 
increased sampling error for a given value of K. To normalize these 
curves for angle to the flow stream, it is necessary to define an "adjusted 
Stokes number" (K') which takes into account the change in projected 



72 



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nozzle diameter with angle. Wien plotted against K', the aspiration 
coefficients for 30, 60 and 90 degrees should approach their tlieoretical 
minima at the same place as the curves for zero misalignment angle and 
anisokinetic sampling velocities (see Figure 6) . 

To develop the adjustment factor for Stokes number, it was neces- 
sary to plot as a function of 0, the value of K where the aspiration 
coefficient reached a value that represented 95% of the maximum error. 
For example the maximum theoretical error for 60 degrees is cos (60) or 
0.5. Therefore the value of K of interest is where there is (.95) (0.5) = 
47.5% sampling error or an aspiration coefficient of 1 - .475 = .525. 
For zero degrees, equations (9) and (10) were solved for R = 0.5 and 
6 = 0.95 to obtain a value of K = 5.9. This velocity ratio was used 
because its theoretical maximum sampling error is 0.5, the same as for 
60 degrees. The values for 60 and 90 degrees were obtained from Figures 
27 and 28 respectively. Because of the flatness of the 30 degree curve 
(it varies only 16% over two and a half orders of magnitude of K) , it was 
not possible to detect exactly when the curve reached 95% of its minimum 
value. Therefore no value for 30 degrees was used in this analysis. 

The equation for the adjusted Stokes number determined from Figure 
29 is 

,. 0.0226 
K' = Ke (22) 

Using this equation it can be determined that the Stokes numbers for 30, 
60 and 90 degrees must be multiplied by 1.93, 3.74 and 7.24 respectively 
to account for the effect of nozzle angle to the flow stream on the 



83 



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a. 






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00 



4 I— 




30 60 

Misalignment Anemic (6) 



90 



Figure 29. Stokes number at which 95% maximum error occurs 
vs. misalignment angle. 



84 



apparent nozzle diameter. Using these correction factors it is possible 
to use the data to determine an expression for 3' in equation (14). Set- 
ting R = 1 and solving for B' this equation becomes 



6'(K'3=4q^ (25) 



Using this expression the experimental data were used to plot B' as a 
function of the adjusted Stokes number K' (see Figure 30) . From this 
plot, it can be observed that the data points for 30, 60 and 90 degrees 
all fall approximately on the same line. It should be noted that most 
of the scatter is due to the 30 degree data and that the amount of the 
scatter is somewhat deceptive. Solving equation (23) for 30 degrees, 
requires that the sampling bias (1-A) must be multiplied by 7.5 to 
normalize it with the 90 degree data. This has an effect of greatly 
increasing any spread in the experimental data. 

To develop a model for inertial sampling bias, it was necessary 
to develop an equation for the line drawn through the data in Figure 30. 
An equation of the form similar to that used by Belyaev and Levin was 
selected to fit the data. 

3'(K',0) = 1 ^—^ (24) 

1 + aK' 

where a and b are constants. The advantage of this equation form is 
that it acts similar to the theoretical expectations of the relationship 
(i.e., 3' approaches zero for very small values of K' and approaches 1 
for very large values of K'). 



85 




c 
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86 



While attempting to determine the constants a and b, it was found 
that the form of the equation had to be altered somewhat to allow g' to 
approach 1 at a faster rate for values of K' greater than 4.0. The fol- 
lowing is tlic final form of the equation selected. 

B'(K',e) = 1 ---i— ^ C25) 

1 + ak' e 

The constants were determined through trial and error to be 0.55 and 0.25 
for a and b respectively. Therefore, the final equation to describe the 
sampling efficiency due to nozzle misalignment as a function of Stokes 
number becomes for R = 1: 

A = 1 + (cose - 1) 3' CK',e) [26) 

where 



CK',e) = 1 _„_i._^_^ (27) 

1 + 0..S5 K'e 



and 



„ 0.0226 
K' = Ke (22) 



Thc;5c equations are solved for 30, 60 and 90 degrees and plotted against 
Stokes number in Figure 31. It can be seen from the graph that the equations 
fit the data within experimental accuracy. Figure 32 is a plot of the 
sampling efficiency for angles between and 90 degrees in 15 degree 
increments . 



87 







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89 



5_^__Th_e_jffect of Nozzle Misalignme nt ar idJ\m^£okJ£iayx__Sa^^ Velocity 

To complete the analysis of anisokinetic sampling, it is necessary 
to know what is the combined effect of both a nozzle misalignment and a 
sampling velocity differing from the free stream velocity. The theoreti- 
cal model predicts that the sampling efficiency will be in the form 

A = 1 + (Rcose - 133" (28) 

where 

3"= f[3(K,R) 3'[K',e}] (29) 

Since the reduction of projected nozzle diameter due to nozzle misalign- 
ment will effect the time available for a particle to change directions 
when sampling at an anisokinetic velocity, the adjusted Stokes number K' 
should also be used in the equation for 3 as well as 3'. Another modifi- 
cation that must be made in the model involves correcting for the fact 
that 3(K',R) does not equal 1 when R = 1. 

B(K',R=l) = l-^-^43j^^ C30) 

To account for this 3'(K',e) must be divided by 3(K',R = 1) so that 
equations (28) £).nd (29) are valid at R = 1. The model to be tested now 
becomes 

A = 1 + (RcosO - 1) 3(K',R) |11^1^51__ (31) 

At first there appears to be an obvious flaw in the model in that the 
aspiration coefficient equals 1 whenever R = l/cos0 regardless of the 



:£%(A.i._a«k 



90 



Stokes number. An example of this is when R = 2 and = 60 degrees. 
This phenomenum can be explained as follows. Since the projected 
frontal area of the nozzle is one half the actual area when 9 = 60 
degrees, in order to sample isokinetically such that there 
is no divergence of streamlines into the nozzle, the sample velocity- 
must be one half of the free stream velocity or R = 2. Therefore, 
the condition of R = l/cos6 defines the condition for obtaining a 
representative sample when the nozzle is misaligned with the flow 
stream. 

Since the sampling methodologies used to determine 3(K,R) and 
3'CK,9) were substantially different [photographic observation vs. 
comparative sampling), it was necessary to see if the two methods 
gave comparable results before the model could be tested. Four sets 
of tests were run with two parallel nozzles; the control nozzle 
sampled isokinetically and the test nozzle sampled anisokinetically . 
Tests were performed at two Stokes numbers (K = 0.154 and K = 0.70) 
and at t\TO velocity ratios (R = 2.3 and R ^ 0.51). The aspiration 
coefficients obtained by comparing the two measured concentrations are 
presented in Figure 33 and Table XIII. The data obtained lie within 
the experimental bounds of the lines produced from Belyaev and Levin's 
data [Equations (5), (9) and (10)]. 

Since the two methods give comparable results, experiments were 
run to test the model. A control nozzle was placed parallel to the 
flow stream and the sampling velocity was set to be isokinetic. The 
test nozzle was inserted at an angle from outside the duct and the 
sampling velocity was set to be either one half or two times the free 



91 






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stream velocity. Tests were run for a range of Stokes numbers from 0.1 
to 1. This range was selected because this was expected to be the area 
where the greatest change in aspiration coefficient occurred. The data 
obtained for R = 2 and R =0.5 for a 60 degree misalignment are presented 
in Tables XIV and XV. Thesedata are plotted and compared with the model's 
prediction in Figure 34. The aspiration coefficient does indeed appear 
to be unity when R = l/cos6 as in the case of R = 2 and 6 = 60 degrees. 
The data for R = 0.5, 9 = 60 degrees appear to approach tlieir theoretical 
limit of Rcose [0.25) at approximately a value of Stokes number of 2 to 5. 
This is near the location that the aspiration coefficient for 9 = 60 
degrees, R = 1 approaches its theoretical limit. This further confirms 
the necessity of using an adjusted Stokes number when the probe is mis- 
aligned with the flow stream. 

To further test the model, experiments were run at 45 degrees 
(R = 2.0 and R = 0.5} and at 30 degrees (R = 2.0). Thesedata presented 
in Tables XVI and XVII are plotted in Figures 35 and 36 also show good 
agreement with the prediction model . 

When tests were run at 9 = 90 degrees, R = 2.1 and K = 0.195 (see 
Table XVIII), an average aspiration coefficient of only 1.5-6 was obtained. 
The value predicted for equation (31) for these conditions is 49%. It 
appears that the model falls apart at 90 degrees for R ^ 1. This is due 
to the fact that when 6 = 90 degrees there is zero projected frontal area 
of the nozzle. This means that subisokinetic sampling could in no way 
produce an increase in concentration as it does when particles lie in 
front of the projected nozzle area. Because of this it is necessary to 
put the condition 9 < 90 degrees on equation (31) . 



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102 



Although the experimental data for 90 degrees do not agree well 
with the prediction model, they do compare favorably with the emperical 
equation of Laktionov (20) [equation (16)]. For the conditions of K = 
0.195 and R = 2.1, his equation predicts as aspiration coefficient of 
3.9%. This comparison is closer than would be expected considering the 
fact that two completely different sampling schemes were used, and 
Laktinov did not analyze the amount of particles collected in the probe. 

It should be pointed out that the term for B'(K',6} does not equal 
1 when 9=0. This means that equation (31) will not be equal to Belyaev 
and Levin's predicting equations (5), (9) and (10) and therefore, equation 
(31) should not be used for 6=0. 

B. Tangential Flow Mapping 

Eight traverse points for the velocity measurements were selected 
according to EPA Method 1 (1) (see Table XIX) . Measurements were made 
using the 5-hole pitot tube at five axial distances from the inlet -- 
ID, 2D, 4D, 8D and 16D, where D is the inner diameter of the duct. At 
each point in the traverse, the pitot tube was rotated until the pres- 
sure differential between pressure taps 2 and 3 (see Figure 25) was 
zero. This angle was recorded as the yaw angle and the pressure readings 
from all five pressure taps were recorded for later calculation of total 
and static pressure, and pitch angle. 

During the initial velocity traverse, a core area was discovered 
in the center of the duct where the direction of the flow could not be 
determined with the pitot tube. The core area was characterized by 
negative readings at all five pressure taps which did not vary much 



TABLE XIX 
LOCATION OF SAI^IPLING POINTS 



103 



Point 

1 
2 

3 
4 

5 



-6 of Diameter 



3 


.3 


10 


.5 


19 


.4 


32 


3 


67 


7 


80. 


6 


89. 


5 


96. 


7 



Distanc e from Wall, 



cm 






.65 


2 


.07 


3 


.S3 


6 


38 


13 


36 


15 


91 


17. 


67 


19. 


09 



Duct Diameter = 19.74 cm 



104 



with the rotation of the probe. Inside the core area it was not possible 
to determine the direction o£ flow because there was no point in the 360 
degree rotation of the probe where the pressures at point 2 and 3 were 
the same. The location of the core area was measured at each location 
along the duct axis and recorded. During the velocity measurements, it 
was observed that the flow was very sensitive to domistream disturbances. 
A crosswind at the end of the pipe produced large fluctuations in the 
pressure measurements. 

Figure 37 shows the graphical interpretation of the pitch and yaw 
components of velocity. The two radii r. and r represent the distance 
from the center of the duct to the outer boundary of the core region. 
The area in the core region was approximated by the following equation: 

c 2 2- 

Tr(r + r^ ) 

A = —^ ^^~ r391 

core 2 ^^-^ 

Tables XX-XXIY show the calculated results of the velocity measure- 
ments at the five axial positions. The low flow was the flow measured 
when a restriction was placed at the inlet of the blower. The restriction 
induced approximately a 40% decrease in the flow rate. The high flow rate 
represented a volumetric flow rate of 15,500 liters per minute, and the 
low flow rate was 11,260 liters per minute. The Revnolds number of the 
system calculated on a basis of the average axial flow rate were 80,000 
and 111,000 for the low and high flow rates respectively. 

After the data were broken dov.Ti, it appeared that data from point 
number 1 did not agree well with the rest of the traverse points. Upon 



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IX 



106 



TABLE XX 

FIVE-HOLE PITOT TUBE MEASUREMENTS 

MADE AT 1 DIAMETER DOlVNSTRE.AiM OF THE CYCLONE 

1-0 Low Flow 

Total Axial Tans^ential 
Anglos, Degrees Velocity Velocity Velocity 
££iBl lAlSk I^ i _ciii/sec cm/sec' cm/sec' 



2 


25.5 


67.9 


70.1 


1786 


608 


1655 


3 


n.o 


77.4 


78.0 


1600 


333 


1561 


4 


+++ 


+ + + 


+++ 


+++ 


+ + + 


+ + + 


5 


3.0 


76.0 


76.0 


1341 


324 


1301 


6 


21.0 


60.0 


62.2 


1761 


821 


1525 


7 


50.0 


51.0 


57.0 


1762 


959 


1369 


8 


32.0 


48.0 


55.4 


1664 


945 


1237 



1-D High Flow 

Total Axial Tangential 

^ . Angles, Degrees Velocity Velocity Velocity 

^21I}1 lllSlL 1^ i cm/sec cm/sec cm/sec 



2 


24.0 


64.0 


66.4 


2782 


1114 


2500 


3 


19.0 


78.5 


79.1 


2348 


444 


2301 


4 


+++ 


+ + + 


+++ 


+ + + 


+++ 


+++ 


5 


3.0 


74.4 


74.4 


1846 


496 


1778 


6 


22.0 


63.8 


65.8 


2699 


1106 


2421 


7 


28. 


57.8 


61.9 


2742 


1292 


2320 


8 


31.0 


54.6 


60.23 


2572 


1277 


2096 



Point No. 1 was too close to the wall to allow insertion of all five 
pressure taps. 

+++ Point lies inside the negative pressure section. 



niVoiVbr. *an*V'l'}ir% 



lo: 



Point 
1 
2 
3 
4 
S 
6 
7 
8 



TABLE XXI 
FIVE -HOLE PITOT TUBE MEASUREMENTS 
MADE AT 2 DIAMETERS DOIVNSTRE.AM OF THE CYCLONE 



2-D Low Flow 



Angles^ Degrees 
Pitch Yaw cf) 



■* ** 



+ + + 



+ •!- + 



■k -x -k 



24.0 60.6 
17.0 73.0 



++ + 



17.0 


64.0 


25.5 


54.4 


30.5 


50.4 



65.2 
58.5 
57.0 



Total 
Velocity 
cm/sec 



+++ 

+++ 
1746 
1761 
1672 



Axial 
Velocity 
cm/sec 



732 
925 
910 



Tangential 

Velocity 

cm/ sec 



63.3 


1754 


788 


1528 


73.8 


1601 


447 


1531 



1569 
1432 
1288 



2-D High Flow 



Angles, Degrees 
Point Pitch ^ Yaw " A 



Total 
Velocity 
cm/sec 



Axial 
Velocity 
cm/sec 



Tangential 

Velocity 

cm/sec 



2 
3 
4 
5 
6 
7 



21.0 
14.0 
+ + + 
37.0" 
16.0 
27.0 
32.0 



60.4 
72.8 
+ + + 
76.0 
64.0 
56.6 
53.6 



62.5 
73. 3 
+ + + 
78.9 
65.1 
60.6 
59.8 



2597 

2276 

+++ 

2057 

2676 

2646 

2621 



1199 
654 
+++ 

396 
1127 
1199 
1318 



2258 

2174 

++ + 

1996 

2405 

2209 

2110 



*** Point No. 1 was too close to the wall to allow insertion of all five 
pressure taps. 

+++ Point lies inside the negative pressure section. 

a This high valve can probably be attributed to one of the pitch pressure 



taps extending into the negative pressure area, 



TABLE XXII 

FIVE -HOLE PITOT TUBE MEASUREfENTS 

MADE AT 4 DIAMETEPSDOV/NSTREAM OF THE CYCLONE 

4-D Low Flow 



108 



3int 


Angl 
Pitch 

*** 


es, De 
Yaw 


grees 

i 
*** 


Total 
Velocity 
cm/sec 

"k "k -k 


Axial 
Velocity 
cm/ sec 

*** 


Tangential 

Velocity 

cm/sec 


1 


*** 


2 


26.0 


49.0 


53.9 


1484 


874 


1120 


3 


15.0 


58.0 


59.2 


1524 


780 


1292 


4 


4.0 


78.0 


78.0 


1144 


238 


1119 


5 


+++ 


+++ 


+ + + 


+++ 


+ + + 


++ + 


6 


13.0 


66.8 


67.4 


1548 


595 


1423 


7 


20.0 


57.2 


59.4 


1592 


810 


1338 


8 


24.5 


54.4 


58.0 


1559 


826 


1268 



4-D High Flow 



Point 


Angl 
Pitch 

*** 


es, Degrees 
Yaw (f) 


Total 
Velocity 
cm/sec 

*** 


Axial 
Velocity 
cm/sec 

*** 


Tangential 

Velocity 

cm/sec 


1 


*** 


2 


25.0 


48.0 


52.7 


2293 


1389 


1704 


3 


16.5 


58.6 


60.3 


2286 


1133 


1951 


4 


3.0 


82.6 


82.6 


1651 


212.6 


1637 


S 


++ + 


+++ 


+++ 


+++ 


+++ 


+++ 


6 


15.0 


68.6 


69.2 


2266 


804 


2110 


7 


20.0 


59.4 


61.4 


2425 


1161 


2087 


8 


27.0 


56.0 


60.1 


2314 


1153 


1918 



Point No. 1 was too close to the wall to allow insertion of all five 
pressure taps. 

+++ Point lies inside the negative pressure section. 



•♦fr*Mfci-<ynn^i*»-*jirft«»^' ■ » ><>■ . -■*a^^.-^rtw^^ 



109 



TABLE XXIII 
FIVE -HOLE PITOT TUBE MEASUREMENTS 

MADE AT 8 DIMETERS DOMSTREAM OF THE CYCLONE 

8-D Low Flow 

Total Axial Tangential 

Angles, Degrees Velocity Velocity Velocity 

l2illl Pitch Yaw ^ cm/sec cm/sec' cm/sec 



2 


19.5 


59.0 


61.0 


1414 


685 


1212 


3 


15.0 


69.0 


70.3 


1436 


484 


1346 


4 


+++ 


+ + + 


+ + + 


+++ 


+++ 


+ + + 


5 


8.0 


63.6 


63.9 


1396 


614 


1250 


6 


20.0 


50.2 


53.0 


1326 


798 


1019 


7 


28.0 


39.4 


47.0 


1289 


879 


818 


8 


29.0 


38. 


46.4 


1231 


849 


758 



8-D High Flow 

Total Axial Tangential 

Mglcs, Degrees Velocity Velocity Velocity 

Point Pitch Yaw ^ cm/sec cm/sec cm/sec 



2 


19.0 


57.0 


59.0 


1875 


966 


1572 


3 


9.0 


70.0 


70.3 


1881 


634 


1767 


4 


+++ 


++ + 


++ + 


+ + + 


+++ 


+++ 


S 





64.6 


64.6 


1743 


748 


1574 


6 


15.0 


50.0 


51.6 


1942 


1206 


1488 


7 


21.0 


43.2 


47.1 


1869 


1272 


1279 


S 


25.0 


42.0 


47.7 


1795 


1208 


1201 



*** Point No. 1 was too close to the wall to allow insertion of all five 
pressure taps. 

+++ Point lies inside the negative pressure section. 



no 



TABLE XXIV 
FIVE-HOLE PITOT TUBE MEASUREMENTS 
MADE AT 16 DIAMETERSDO'A'NSTREA.M OF THE CYCLONE 

16-D Low Flow 

Total Axial Tangential 
Angles, Degrees Velocity Velocity Velocity 
Point Pitch Yaw cm/sec cm/sec cm/sec 



2 


27.0 


34.0 


42.4 


1073 


729 


600 


3 


19.0 


41.0 


44.5 


1169 


834 


767 


4 


9.0 


58.6 


59.0 


1014 


522 


865 


5 


+ + + 


+++ 


+ + + 


+ + + 


+++ 


+ + + 


6 


13.0 


63.0 


63.7 


929 


412 


828 


7 


17.0 


50.4 


52.3 


1205 


735 


928 


8 


18.0 


47.6 


50.11 


1190 


763 


979 



16-D High Flow 

Total Axial Tangential 

Angles, Degrees Velocity Velocity Velocity 

Point P-il^Jl 1^ i. cm/sec cm/sec_ _ cm/sec 

-r *** *** *** *** *** *** 



2 


22.5 


36.4 


42.0 


1553 


1154 


921 


3 


21.0 


44.0 


47.8 


1653 


1110 


1148 


4 


9.0 


66.0 


66.3 


1513 


608 


1382 


5 


+ + + 


+++ 


++ + 


+++ 


+++ 


+ + + 


6 


12.0 


61.2 


61.9 


1675 


789 


1468 


7 


20.0 


53.4 


55.9 


1755 


983 


1407 


8 


19.0 


49.0 


51.7 


1739 


1078 


1312 



*** Point No. 1 was too close to the wall to allow insertion of all five 
pressure taps. 

+++ Point lies inside the negative pressure section. 



Ill 



checking the measurement setup, it was discovered that because of the 
construction of the probe and the closeness of the first traverse 
point to the opening, one of the pitch pressure points was not completely 
in the flow stream. Because of this, data from traverse point number 1 
c'lrenot presented with the rest of the data. 

The velocity measurements at the other traverse points for both 
flow rates and all five axial distances showed approximately the same 
characteristics. The pitch angle increased from the core area to the 
duct wall. The yaw angle and the combined angle 4) decreased from the 
core area to the walls. At the inlet and up to eight diameters down- 
stream, angles as high as 70 degrees were found near the core area of 
the flow field. The total velocity, axial velocity, and the tangential 
velocity all showed the same cross sectional flow pattern. The velocities 
were minimum at the core, increased with radius and then slightly decreased 
near the wall. These patterns are similar to those found in the swirling 
flow generated with fixed vanes (23) . 

In order to observe the changes in the flow as a function of axial 
distance from the inlet, the cross sectional averages of the angle c(), 
core area, and tangential velocity were calculated and presented in Table 
XXV and plotted in Figures 38 and 39. All three parameters show a very 
gradual decay of the indicators of tangential flow as was expected from 
the reported tests (23). The curves have the same shape for both flow 
rates . 

The high core area for the measurements at 16 diameters downstream 
was confirmed by repeated measurements. These values may be due to a 



u: 



TABLE XXV 
AVERAGE CROSS SECTIONAL VALUES 
AS A FUNCTION OF DISTANCE DOWNSTREAM AND FLOW RATF 



Average Values for High Fl 



ow 



Diameters <f) Location of* Tangential Velocity Core Area 

Downstream [degrees) Core A rea (ctti) (cm/s ec) (cm') 

1 68.0 5.40 - 13.04 2223 

2 66.7 5.78 - 13.22 2190 
4 64.3 6.79 - 13.93 1901 
8 56.7 5.58 - 12.51 1480 

i6 54.3 7.43 - 14.62 1273 



Average Values for Low Fl 



ow 



47 


.23 


43 


94 


40 


78 


38 


26 


44 


78 



Diameters tf) Location of* Tangential Velocity Core Area 

Downstream [degrees) Core Ar ea (cm) (cm/sec) 

1 66.45 5.42 - 12.87 1441 

2 63.5 5.85 - 13.07 1469 
4 62.7 7.05-13.93 1260 
8 56.9 5.65 - 12.25 1067 

16 52.0 7.99 14.69 811 



(cm^) 


45 


.16 


41 


.39 


38 


45 


37 


03 


42 


13 



* Center of the duct is at 9.87 



cm. 



(]orc Area 



113 



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115 



disturbance effect of the end of the duct which was only a few diameters 
downstream of the sampling point. The increase in average tangential 
velocity at 2 diameters from the inlet can be attributed to the fact 
that two of the traverse points were within the core area. It can be 
seen from the other profiles that the inner points had lower velocity 
values, and therefore the exclusion of the inner points would lead to a 
higher velocity average. 

Plotted in Figure 40 is the location of the core area with respect 
to the duct center. It can be seen that the swirling flow is indeed not 
axisymmetric and the location of the core area changes location with 
axial distance. Only one drawing is used to represent the situation for 
both high and low flow rate because the location for both conditions was 
almost identical. 



116 



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-*w^^l«*»-\w^>,.i^ =- ,^ ** i.-j. - . -•* - 



CHAPTER V 

SIMULATION OF AN EPA METHOD 5 EMISSION TEST 

IN A Ty\NGENTIAL FLOW STREMI 

A model has been developed and tested which describes particle 
collection efficiency as a function of particle characteristics, angle 
of misalignment, and velocity ratio. Together with the measurement of 
velocity components in a swirling flow it is possible to analyze the 
emission rate errors that would occur when performing a Method 5 
analysis of the effluent stream following a cyclone. 

For this simulation analysis, the volumetric flow rate and iso- 
kinetic sampling velocities are calculated from velocity measurements 
obtained at the eight diameter sampling location using a S-ty|5e pitot 
tube (see Tables XXVI and XXVII). The angle cf), velocity ratio, and 
particle velocity are determined from velocity measurements made at 
the same location using the five-hole pitot tube (see Tabic XXII). 
The particle characteristics are obtained from particle size distribution 
tests made by Mason (22) on basically the same system. From a particle 
distribution with a 3.0 ym MMD and geometric standard deviation of 2.13 
(see Figure 41), ten particle diameters were selected which represent 
the midpoints of 10% of the mass of the aerosol (see Table XXVIII). The 
density of the particles was assumed to be 2.7 g/cm-^. The nozzle diameter 
was selected using the standard criteria to be 0.635 cm (1/4 inch). In 
the model it was assumed that the nozzle would be aligned parallel with 
the axis of the stack, and therefore, G = (J) . 



117 



118 



TABLE XXVI 
S-TYPE PITOT TUBE MEASUREMENTS 
MADE AT THE S-D SAMPLING PORT FOR THE LOW FLOW CONDITION 



Point 


Dynamic 
Pressure 
(cm H^O) 


Static 
Pressure 
(cm H^O) 


Ap 

(cm H^O) 


(cm H^O) ' 


Velocity 
(cm/sec) 


8 


0.96 


-0 . 36 


1.32 


1.15 


1229.0 


7 


0.99 


-0.48 


1.47 


1.21 


1298.5 


6 


0.66 


-0.89 


1.55 


1.24 


1331.6 


5 


-1.07 


-0.74 


0.33 


0.57 


614.7 


4 


-1.32 


-1.04 


-0.2S 


-0.53 


-565.6 


3 


-0.41 


-0.46 


0.05 


0.22 


241.1 


2 


0.30 


-0.17 


0.47 


0.69 


743.2 


1 


0.69 


-0.10 


0.79 


0.89 


949.3 



119 



TABLE XXVII 
S-TYPE PITOT TUBE MEASUREMENTS 
MADE AT THE 8-D SAMPLING PORT FOR THE HIGH FLOW CONDITION 



Point 


Dynamic 
Pressure 
(cm H^O) 


Static 
Pressure 
(cm H^O) 


Ap 
(cm H^O) 


(cm H^O] ' 


Velocity 
(cm/sec] 


8 


2.03 


-0.66 


2.69 


1.64 


1755.4 


7 


1.83 


-1.57 


3.40 


1.84 


1974.7 


6 


1.17 


-2.23 


3.40 


1.84 


19 74.7 


5 


-2.26 


-2.79 


0.53 


0.73 


781.3 


4 


-1.83 


-1.32 


-0.51 


-0.71 


-762.5 


3 


-0.89 


-1.02 


0.13 


0.36 


381.2 


2 


0.61 


-0.43 


1.04 


1.02 


1091.7 


1 


0.91 


-0.10 


1.02 


1.01 


1078.3 



|«l^»-«T:■T*^l•*'■?«1»vl.|■rfEfl,■:;»^.^f»^•««*p♦•*> •ip»l»*■^i^— • . 



120 




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TABLE XXVIII 
MIDPOINT PARTICLE DIAMETERS 
FOR THE 10 PERCENT INTERVALS OF THE MASS DISTRIBUTION 
MMD = jym a = 2. 13 



121 



Range 

- 10 

10 - 20 

20 - 30 

30 - 40 
40 - 50 
50 - 60 
60 - 70 
70 - 80 
SO - 90 
90 - 100 



Midpoint 
5 
15 
25 
35 
45 
55 
65 
75 
85 
95 



^mici 
(]} meters) 


7 
Dp-C 


0.84 


0.84 


1.32 


1.96 


1.75 


3.35 


2.20 


5.20 


2.70 


7.73 


3.25 


11.09 


4.00 


16.65 


4.90 


24.80 


6.60 


- 44.63 


10.40 


109.84 



122 



Using these parameters the average aspiration coefficients are 
determined at each traverse point using the ten particle dianeters and 
equations (33) - (39) . 



A,(R,.*,,K,) = .lA„p3.^* -IVls, - -I'V,, 



^3f«3-*3'^3) = -'V* * -''Vis?, * -IVS'. 



+ 



" ■iVs% 


(53) 


■'^■'^Dp95% 


(34) 


•■ 


(35) 


• 


(56) 


• 


(37) 


• 


(38) 


" -'Vs-o 


(39) 



A (R (f) K ) = .lA^ ^, + .1A„ ,,„ + .lA + 
o b S 8 Dp5% DplS'o Dp25°; 

Where A^ = total aspiration coefficient for traverse point i. 
R^ = (total velocity at i)/(sampling velocity at i) . 
<i> = angle of flow at point i relative to the axis of the stack. 
K.j^= Stokes number based on the nozzle diameter, total velocity 
at i, and particle diameter Dp,,,,. 

K'ci 

Dpj^„,= Midpoint particle diameters each representing 10% of the 
total mass. 
Since the sampling velocity will determine the volume of air sampled at 
each traverse point, the total aspiration coefficient for each flow rate 
is determined by taking an average weighted according to sampling velocity. 

A = — - ^^ ^-^ -'' 'j-5 5 i ^_A__iZlX_JiO. 
^ v.„ + \' . TTYT^TV. , + v"~T^ ^^ ^40) 

i2 lo i5 i6 17 18 



Where (^'.);= inlet velocity at traverse point j. 

Because of the missing data at point 1 and negative pressure section at 

point 4, these tw^o traverse points were not used in the analysis. 



12: 



The total aspiration coefficients calculated in this raanner for 
the low and high flow rates were 0.937 and 0.906 respectivelv (see 
Table XXIX and XXX). There are two reasons for the relative low amounts 
of concentration error found in this analysis. One reason is that the 
two mechanisms causing sampling error, nozzle misalignment and aniso- 
kinetic sampling velocities, cause errors in the opposite direction. 
The S-type pitot tube detected a velocity less than or equal to the 
actual velocity which would lead to subisokinetic sam.pl ing producing 
an increased concentration. The nozzle misalignment when sampling 
parallel to the stack wall would produce a decreased concentration. So 
each of these errors has a tendency of reducing the other error. 

Another reason for the small errors was the small size of the 
aerosol. The Stokes numbers for over 50% of the particles were less 
than 0.2 and 0.3 for the low and high flow rates respectively. These 
values lead to small sampling errors, even when isokinetic sampling 
conditions are not maintained. 

Mason experimentally determined that the collection efficiency should 
be on the order of 50% (22) . Since the flow rate used by Mason was ap- 
proxim.ately midway between the high and low flow rate in this study, the 
flow patterns should be approximately the same. The discrepancy between 
Mason's experimental values and the values predicted by the simulation 
probably can be accounted for as experimental error by Mason. It would 
be nearly impossible to obtain a 50% sampling error for an aerosol as 
small as the one used without extreme anisokinetic sampling conditions. 
Mason also found a 40% error when sampling at the angle associated with 



TABLE XXIX 
ASPIRATION COEFFICIENTS 
CALCULATED IN THE SIMULATION MODEL FOR THE LOW FLOW CONDITION 



124 



Point 



Sampling Velocity True Velocity 
from S-Type Pitot from 5 -Hole Pitot cp 
JTube (cm/sec) Tube (cm/ sec] Degrees 



Ci/Co % 



1 
2 

3 
4 
5 
6 
7 
8 



949.3 

743.2 

241.1 

++ + 

614.7 

1351,6 

1298.5 

1229.0 



1414 
1436 
+ + + 
1396 
1326 
1289 
1231 



61.0 


1.9 


97.0 


70.3 


6.0 


142.0 



63.9 


2.3 


100.5 


53.0 


1.0 


86.5 


47.0 


0.99 


90.1 


46.4 


1.0 


90.7 



Weighted Average 



93.7 






125 



TABLE XXX 
ASPIRATION COEFFICIENTS 
CALCULATED IN THE SIMULATION MODEL FOR THE HIGH FLOW CONDITION 



Sampling Velocity True Velocity 
from S-Type Pitot from 5-Hole Pitot (^ 
Point Tube (cm/sec) Tube (cm/sec) Degrees R Ci/Co% 



1875 
ISSl 



1743 64.6 2.20 97.60 

1974.7 1942 51.6 0.98 84.10 

1974.7 1869 47.1 0.95 86.30 

1755.4 1795 47.7 1.02 88.50 



1 


1078.3 


2 


1091.7 


3 


381.2 


4 


+++ 


5 


7SI.3 



59.0 


1.72 


95.06 


70.3 


4.90 


131.85 



Weighted Average = 90.6 



126 



the maximum Ap. From Figure 15 it is apparent that by splitting the 
difference between the angles where the velocity pressure drops off 
rapidly, it should be possible to get within 20 degrees of the zero 
yaw angle. This means that the sample velocity measured by the S-type 
pitot tube will be approximately the same as the true total velocity 
and therefore, the sampling error should be no greater than the cosine 
of 20 degrees or 0.94. This would represent the maximum error for a 
very large aerosol and would be much less for the aerosol used in the 
study. Since Mason's sampling error is almost ten times as high as 
the theoretical maximum, it must be attributed to some flaw in the 
experi.mental setup. 

In order to see how much greater the error would be for larger 
particles, a similar analysis was performed using a distribution with 
a 10 ym mass mean diameter and 2.5 geometric standard deviation (see 
Figure 411. This was the distribution obtained at the outlet of a 
cyclone in a hot-mix asphalt plant (45). Because of the larger diameter 
particles the sampling efficiency was reduced to 0.799 for the high flow 
condition. 

The volumetric flow rates determined from the S-type pitot tube 
measurements are compared with the flow rates calculated from five-hole 
pitot tube measurements in Table XXXI. The axial flow rates using the 
five-hole pitot tube data are cal culated by multiplying the average axial 
velocity by the inner duct area minus the core area. The flow rates 
using the S-type pitot tube data were determined using two different 
methods varying in how the negative velocity at port four is handled. 



iw-... •■■ >Sa«iei. ^-- 



127 



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128 



In the first method, the negative velocity is not used to determine 
the average axial velocity. The volumetric flow rate is calculated by 
multiplying the average axial velocity by 7/8th of inner cross sectional 
area. In the second method, the negative value is used in the determi- 
nation of the average velocity and the entire inner duct area is used to 
determine the flow rate. ■ 

The results presented in Table XXX, show that the insensitivity of 
the S-type pitot tube to yaw angle produces a higher calculated flow 
rate by approximately 28%. By incorporating the negative velocity in 
the average velocity determination, this error is reduced to 17%. 

It should be noted that the S-type pitot tube data fit very well 
what would be expected from looking at the sensitivity of the pitot 
tube to yaw angle [Figure 15). When the traverse point had a yaw angle 
less than approximately 45 degrees, the S-type pitot tube readings were 
very close to the total velocity. However, beyond angles of 45 degrees 
the pitot tube readings drop off quite rapidly and at 70 degrees, the nitot 
tube was reading a value of less than one fifth of the true value. 

The errors for both sampling efficiency and flow rate determination 
are presented in Table XXXI for the three simulated conditions. The 
sampling errors and flow rate errors are in opposite direction so that 
when the two values are combined to determine emission rate, the overall 
effect is reduced. 



CHAPTER VI 
SUNMARY AND RECOf-MENDATIONS 

A. Suiiimarv 



Results o£ experiments in this study liave led to a better understanding 
of the types and magnitude of errors that are involved when attempting to 
obtain a representative sample of particulate matter from gas streams with 
complex flow patterns. The errors induced by tangential flow were analyzed 
from two separate approaches. The first involved analysis of particle sam- 
pling error as a function of particle characteristics, sampling velocity 
relative to the flow stream velocity, and angle of the nozzle relative to the 
direction of flow. The second involved analysis of swirling flow patterns and 
their subsequent effect on flow measurements made by the S-type pitot tube. 

Particle sampling errors as a function of velocity ratio and angle of 
misalignment were studied by taking comparative anisokinetic and isokinetic 
samples from a straight section of duct. By analyzing the problem in this 
method the data obtained are more useful and have many more applications 
beyond this study. They provide fundamental information for a better under- 
standing of the inertial effects in aerosol sampling. 

The flow measurement errors were analyzed by mapping the exact flow 
pattern at the exit of a cyclone using a five-hole pitot tube. Cross sec- 
tional profiles were measured at five axial distances along the stack to 
determine how the flow pattern changes as it moves up the stack. S-type 
pitot tube measurements were taken and compared to the results of the 
five-hole pitot tube measurements. 



129 



150 



The two aspects of this study, anisokinetic sampling errors and 
flow measurements, were combined in a simulation model to determine the 
magnitude of errors when an EPA Method 5 emission test is performed at 
the exit of a cyclone. 

A summary of the important results determined from this study is 
as follows: 

A. The flow patterns found in a stack following the exit of a 
small industrial cyclone are of such a nature that it makes it extremely 
difficult to obtain a representative sample with the present EPA recom- 
mended equipm.ent. Angles in excess of 70 degrees relative to the stack 
axis are found in some parts of the flow. Since large scale turbulence, 
such as swirling flow, is inherently self-preserving in round ducts, it 
decays very slowly as it moves up the stack and therefore sampling at 
any location downstream of the cyclone will involve the same problems. 

B. The yaw characteristics of the S-type pitot tube lead to several 
types of errors when used in a tangential flow stream. When the angle 

of yaw is less than 45 degrees, the measured velocity is greater than or 
equal to the actual velocity with the maximum error being approximately 
5%. Beyond 45 degrees the measured velocity drops off quite rapidly and 
at an angle of 70 degrees the measured velocity is less than half the 
true velocity. Because of its yaw characteristics, the S-type pitot tube 
is not suitable for distinguishing the axial component of flow from the 
total flow which includes the tangential component. Volumetric flow 
calculations based on S-type pitot tube measurements in a swirling flow 
were found to be in excess of the actual flow by as m.uch as 50°„. 



131 



C. Pitot tubes based on the five-hole and three-hole designs are 
useful tools in determining the velocity components in a tangential 
flow field. The five-hole pitot tube has the advantage of giving pitch 
information as well as the yaw angle. However, in a cyclonic flow 
stream, the yaw angle is of m.uch greater magnitude than the pitch angle 
and therefore, the pitch angle can be ignored with small error. In the 
situation modeled, if pitch angle were ignored, the calculated flow rate 
would be in error by less than 6%. 

D. The particle sampling errors due to anisokinetic sampling 
velocity and nozzle misalignment were analyzed and a model was developed 
to describe the sampling efficiency as a function of velocity ratio (R) , 
misalignment angle [6], particle diameter, particle velocity, and nozzle 
diameter. It was found that the maximum error for R = 1, approached 
(1 - cose). When both a nozzle misalignment and anisokinetic sampling 

velocities are involved then the maximum error approaches \l - Rcos9|. 

The equations and their limiting conditions for predicting the aspiration 

coefficient are summarized in Table XXXII. 

E. The Stokes number adequately describes the inertial character- 
istics of particle sampling. However, when the nozzle is misaligned to 
the flow stream, there is an apparent change in the inertial properties 
which is due to a reduced projected nozzle diameter. A correction factor 
was developed to adjust the Stokes number to take this into account. 

F. When the probe wash was analyzed separately from the filter, 

it was found that as much as 60% of the total particulate matter enterin- 



152 



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the nozzle was collected on the nozzle walls. This has implications 
not only on the importance of using the probe wash in the analysis, 
but more importantly it implies that there may be possible problems 
in obtaining accurate particle size data using a device such as an 
impactor. If the collection of particles in the nozzle is particle 
size dependent, then losses in the probe could lead to particle 
sizing errors. 

G. A simulation model was developed which incorporates the 
information obtained in this study on particle sampling errors and 
the flow mapping data. The particle sampling efficiency in a 
tangential flow stream was, as expected, a function of particle size. 
For a particle distribution with a mass mean diameter [MMD) of 3.0 
ym and a geometric standard deviation of 2.15, the sampling errors 
predicted were less than 10%. For a larger distribution with a mass 
mean diameter of 10.0 ym and geometric standard deviation of 2.3, a 
20% sampling error was predicted. One of the reasons that the sampling 
errors were as small as these were, is that the two mechanisms inducing 
sampling bias produce errors in opposite directions. The misalignment 
of the nozzle caused by the tangential velocity component leads to a 
reduction of sample concentration. The reduced sampling velocity, 
calculated from S-type pitot tube measurements, leads to subisokinetic 
sampling and an increased sample concentration. When these two mechanism.s 
are combined, the total error is reduced somewhat depending upon the 
magnitude of the two errors. 



134 



B. Recomm endatio ns 

EPA recommends that if the average angle of the flow relative to 
the axis of the stack is greater than 10 degrees, then EPA Method 5 
should not be performed. Since the maximum error in particle sampling 
has been found to be (1 - RcosO) , the 10 degree requirement is unduly 
restrictive and a 20 degree limitation would be more appropriate. For 
a 20 degree angle, the velocity measured by the S-type pitot tube would 
be approximately the same as the true velocity (i.e., R = 1] . Therefore, 
the maximum error would be (1 - cos 20°) or 6% for a very large aerosol. 

When cyclonic flow does not exist in a stack, EPA recommends 
either straightening the flow or moving to another location. Because 
of the physical limitations of these suggestions, a better approach 
would be to modify Method 5 so that it could be used in a tangential 
flow stream. By replacing the S-type pitot tube with a three-hole 
pitot tube, the direction of the flow could be accurately determined 
for aligning the nozzle, and the velocity components could be measured 
for a correct calculation of volumetric flow rate. In addition to the 
three-hole pitot tube, the modification would have to include a pro- 
tractor to measure the flow angle, an extra manometer, and a method of 
rotating the probe without rotating the entire impinger box. 



REFERENCES 



1. Standards o£ Performance for New Stationary Sources. Federal Register, 
36(247} :24876, 1971. 

2. Revision to Reference Method 1-8. Federal Register, 42(160) :41754 , 1977. 

3. Wilcox, J. D. Isokinetic Flow and Sampling of Airborne Particulates. 
Artificial Stimulation of Rain. Pergamon Press, New York, 1957, p. 177. 

4. Lapple, C. E. and C. G. Shepherd. Calculation of Particle Trajectories. 
Ind. Eng. Chem. , 32(5) :605, 1940. 

5. Watson, 11. H. Errors Due to Anisokinetic Sampling of Aerosols. Amer. 
Ind. Hyg. Assoc. Quart., 15(1) :21, 1954. 

6. Dennis, R. , W. R. Samples, D. M. Anderson and L. Silverman. Isokinetic 
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7. Hemeon, W. C. L. and G. F. Haines, Jr. The Magnitude of Errors in 
Stack Dust Sampling. Air Repair, 4(3):159, 1954. 

8. Whiteley, A. B. and L. E. Reed. The Effect of Probe Shape on the 
Accuracy of Sampling Flue Gases for Dust Content. J. Inst. Fuel, 
32:316, 1959. 

9. Lundgren, D. A. and S. Calvert. Aerosol Sampling with a Side Port 
Probe. Amer. Ind. Hyg. Assoc. J., 28(3) :208, 1967. 

10. Badzioch, 8. Collection of Gas-Borne Dust Particles by Means of an 
Aspirated Sampling Nozzle. Brit. J. Appl. Phys . , 10:26, 1959. 

11. Fuchs, N. A. The Mechanics of Aerosols. The Macmillan Co., New York, 
1964, p. 73. 

12. Belyaev, S. P. and L. M. Levin. Investigation of Aerosol Aspiration 
by Photographing Particle Tracks Under Flash Illumination. J. Aerosol 
Sci., 5:127, 1972. 

13. Belyaev, S. P. and L. M. Levin. Techniques for Collection of Representa- 
tive Aerosol Samples. J. Aerosol Sci., 5:325, 1974. 



135 



156 



14. Davies, C. N. The Entry of Aerosols into Sampling Tubes and Heads. 
Brit. J. Appl. Phys., Ser. 2, 1:921, 1970. 

15. Martone, J. A. Sampling of Submicrometer Particles Suspended in Near 
Sonic and Supersonic Free Jets of Air. Presented at the Annual Meeting 
of the Air Pollution Control Association, Toronto, Canada, 1977. 

16. Sehmel, G. Particle Sampling Bias Introduced by Anisokinetic Sampling 
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31(6) :758, 1970. 

17. Glauberman, II. The Directional Dependence of Air Samplers. Amer. Ind. 
Hyg. Assoc. J., 25(3). -235, 1962. 

18. Raynor, G. S. Variation in Entrance Efficiency of a Filter Sampler with 
Air Speed, Flow Rate, Angle and Particle Size. ,Amer. Ind. Hyg. Assoc. 
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19. Fuchs, N. A. Sampling of Aerosols. Atmos . Envir., 9:697, 1975. 

20. Laktionov, A. G. Aspiration of an Aerosol into a Vertical Tube from a 
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21. Vitols, V. Theoretical Limits of Errors Due to Anisokinetic Sampling of 
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22. Mason, K. W. Location of the Sampling Nozzle in Tangential Flow. M. S. 
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23. Baker, D. W. and C. L. Sayre. Decay of Swirling Turbulent Flow of Incom- 
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24. Chigier, N. A. Velocity Measurement in Vortex Flows. Flow: Its Measure- 
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25. Hanson, H. A. and D. P. Saari. Effective Sampling Techniques for 
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W|4"«-^ >— .^^^l^iHl •- 



137 



27. Grove, D. J. and W. S. Smith. Pitot Tube Errors Due to Misalignment and 
Nonstreamlined Flow. Stack Sampling News, November, 1973. 

28. Hanson, H. A., R. J. Davini, J. K. Morgan and A. A. Iversen. Particulate 
Sampling Strategies for Large Power Plants Including Nonuniform Flow. 
EPA-600/2-75-170, U. S. Environmental Protection Agency, Research Triangle 
Park, N.C. , 1976, 349 pp. 

29. Williams, F. C. and F. R. DeJarnette. A Study on the Accuracy of Type S 
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Research Triangle Park, N.C, 1977. 

30. Lea, J. F. and D. C. Price. Mean Velocity Measurements in Swirling Flow 
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31. Green, H. L. and W. R. Lane. Particulate Clouds: Dusts, Smokes and 
Mists. E. F. M. Spon. Ltd., London, 1957, p. 36. 

32. Air Pollution Manual. Part II - Control Equipment. Amer. Ind. Hyg. 
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33. IVhitby, K. T., D. A. Lundgren and C. M. Peterson. Homogeneous Aerosol 
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34. Perry, J. K. Chemical Engineers' Handbook, McGraw-Hill, New York, 1941. 

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37. Doebelin, E. 0. Measurement Systems, Application and Design. McGraw- 
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38. Smith, F. H. The Effects of Nozzle Design and Sampling Techniques on 
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39. Manual of Fluorometric Clinical Procedures. G. K. Turner Association, 
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40. American Institute of Physics Handbook. D. E. Gray, Ed., McGraw-Hill, 
New York, 1957. 



15S 



41. Sehmel, G. A. The Density of Uranine Particles Produced by a Spinning 
Disc Aerosol Generator. Amer. Ind. Hyg. Assoc. J., 28C5):491, 1967. 

42. Source Sampling Workbook. Control Programs Development Division, Air 
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BIOGRAPHICAL SKETCH 

Michael Durham v\(as born on December 11, 1949, in Key West, Florida. 
Being a member of a Navy family, he was constantly on the move and 
attended eight different grade schools and two high schools in Hawaii, 
Virginia, California and Kentucky. He studied two years at Texas Af,M 
University and tlien two at the Pennsylvania State University where he 
received a B.S. in Aerospace Engineering in 1971. His next three years 
were spent working with tlie National Academy of Science and the American 
Psychological Association in Washington, D.C. In September 1974 l:e began 
his graduate education in Environmental Engineering Sciences at the 
University of Florida. After receiving a Master of Engineering in 
August of 1975, he stayed on at the university as a graduate research 
assistant in pursuit of a Ph.D. for three years, the result of which is 
this dissertation. 



139 



I certify that I have read this study and that in my opinion it 
conforms to acceptable standards of scholarly presentation and is fully 
adequate, in scope and quality, as a dissertation for the degree of 
Doctor of Philosophy. 




^yU-neig^yU -^ _ 



Dale A. Lundgren, Chairrnrm 
Professor of Environmental 
Engineering Sciences 



I certify that I have read this study and that in my opinion it 
conforms to acceptable standards of scholarly presentation and is fully 
adequate, in scope and quality, as a dissertation for the degree of 
Doctor of Philosophy. 




'^'7 (^.(^ 



-c^C„ 



Paul Urone 
Professor of Environmental 
Engineering Sciences 



I certify that I have read this study and that in my opinion it 
conforms to acceptable standards of scholarly presentation and is fully 
adequate, in scope and quality, as a dissertation for the degree of 
Doctor of Philosophy. 



'^-V^ 



^1 



L 



\ 



Wayne /C. Huber 
Professor of Environmental 
Engineering Sciences 



I certify that I have read this study and that in my opinion it 
conforms to acceptable standards of scholarly presentation and is fully 
adequate, in scope and quality, as a dissertation for the degree of 
Doctor of Philosophy. 









■') 



/i-ry oicc.;. 



Alex E. Green 

Graduate Research Professor of 
Physics and Nuclear Engi- 
neering Sciences 



This dissertation was submitted to the Graduate Faculty of the College 
of Engineering and to the Graduate Council, and was accepted as partial 
fulfillment of the requirements for the degree of Doctor of Philosophy. 



Auaust, 197{ 



lUu- a. /f. 



-«.«&, 



Dean^ College of Engineering 



Dean, Graduate School